GH-20161: [Website] Remove mentions of master branch from Apache Arrow website content (#324)

# Overview

As part of apache/arrow#31142 and in response to the [recent rename of
the `apache/arrow-site` repository default branch to
`main`](https://issues.apache.org/jira/browse/INFRA-24242), this pull
request removes mentions of the "master" branch from the Apache Arrow
website content.

# Qualification

To qualify these changes, I:

1. Performed a local build and preview of the website using `bundle exec
rake` and manually verified that all the links are still working.

# Future Directions

1. There are still some remaining tasks listed in apache/arrow#31142
related to the renaming of the default branch of the `apache/arrow` repo
(and related repositories) to `main`.

# Notes

**Note**: I left the mentions of "master" in the `_release` and `_posts`
directory unmodified. As described in
https://github.com/apache/arrow/issues/20161#issuecomment-1442307810,
it's unclear whether it makes sense to change these uses since these are
referring to a past state of the repository. If the community would
prefer that we also removes mentions of "master" from these directories,
I would be more than happy to do so.

Closes apache/arrow#20161.
diff --git a/README.md b/README.md
index 1b0cfec..320d373 100644
--- a/README.md
+++ b/README.md
@@ -64,7 +64,7 @@
 
 ## Deployment
 
-On commits to the `master` branch of `apache/arrow-site`, the rendered
+On commits to the `main` branch of `apache/arrow-site`, the rendered
 static site will be published to the `asf-site` branch using GitHub
 Actions. On a fork, it will deploy to your `gh-pages` branch for
 deployment via GitHub Pages; this is useful for previewing changes
diff --git a/_includes/header.html b/_includes/header.html
index 94d9c5d..0e4a9aa 100644
--- a/_includes/header.html
+++ b/_includes/header.html
@@ -36,15 +36,15 @@
             <hr/>
             <a class="dropdown-item" href="{{ site.baseurl }}/docs/c_glib">C GLib</a>
             <a class="dropdown-item" href="{{ site.baseurl }}/docs/cpp">C++</a>
-            <a class="dropdown-item" href="https://github.com/apache/arrow/blob/master/csharp/README.md">C#</a>
+            <a class="dropdown-item" href="https://github.com/apache/arrow/blob/main/csharp/README.md">C#</a>
             <a class="dropdown-item" href="https://godoc.org/github.com/apache/arrow/go/arrow">Go</a>
             <a class="dropdown-item" href="{{ site.baseurl }}/docs/java">Java</a>
             <a class="dropdown-item" href="{{ site.baseurl }}/docs/js">JavaScript</a>
             <a class="dropdown-item" href="https://arrow.juliadata.org/stable/">Julia</a>
-            <a class="dropdown-item" href="https://github.com/apache/arrow/blob/master/matlab/README.md">MATLAB</a>
+            <a class="dropdown-item" href="https://github.com/apache/arrow/blob/main/matlab/README.md">MATLAB</a>
             <a class="dropdown-item" href="{{ site.baseurl }}/docs/python">Python</a>
             <a class="dropdown-item" href="{{ site.baseurl }}/docs/r">R</a>
-            <a class="dropdown-item" href="https://github.com/apache/arrow/blob/master/ruby/README.md">Ruby</a>
+            <a class="dropdown-item" href="https://github.com/apache/arrow/blob/main/ruby/README.md">Ruby</a>
             <a class="dropdown-item" href="https://docs.rs/crate/arrow/">Rust</a>
           </div>
         </li>
diff --git a/community.md b/community.md
index 3bde837..4a98072 100644
--- a/community.md
+++ b/community.md
@@ -52,7 +52,7 @@
 
 <ul>
   <li> <code>issues@</code> for the creation of GitHub issues {% include mailing_list_links.html list="issues" %} </li>
-  <li> <code>commits@</code> for commits to the <a href="https://github.com/apache/arrow">apache/arrow</a> and <a href="https://github.com/apache/arrow-site">apache/arrow-site</a> repositories (typically to <code>master</code> only) {% include mailing_list_links.html list="commits" %} </li>
+  <li> <code>commits@</code> for commits to the <a href="https://github.com/apache/arrow">apache/arrow</a> and <a href="https://github.com/apache/arrow-site">apache/arrow-site</a> repositories (typically to <code>main</code> only) {% include mailing_list_links.html list="commits" %} </li>
   <li> <code>builds@</code> for nightly build reports {% include mailing_list_links.html list="builds" %} </li>
 </ul>
 
diff --git a/index.html b/index.html
index 1c65e82..9e80079 100644
--- a/index.html
+++ b/index.html
@@ -14,7 +14,7 @@
   <div class="col-lg-4 mt-3">
       <h3>Libraries</h3>
       <p>Arrow's libraries implement the format and provide building blocks for a range of <a href="{{ site.baseurl }}/use_cases/">use cases</a>, including high performance analytics. <a href="{{ site.baseurl }}/powered_by/">Many popular projects</a> use Arrow to ship columnar data efficiently or as the basis for analytic engines.</p>
-      <p>Libraries are available for <a href="{{ site.baseurl }}/docs/c_glib/">C</a>, <a href="{{ site.baseurl }}/docs/cpp/">C++</a>, <a href="https://github.com/apache/arrow/blob/master/csharp/README.md">C#</a>, <a href="https://godoc.org/github.com/apache/arrow/go/arrow">Go</a>, <a href="{{ site.baseurl }}/docs/java/">Java</a>, <a href="{{ site.baseurl }}/docs/js/">JavaScript</a>, <a href="https://arrow.juliadata.org/stable/">Julia</a>, <a href="https://github.com/apache/arrow/blob/master/matlab/README.md">MATLAB</a>, <a href="{{ site.baseurl }}/docs/python/">Python</a>, <a href="{{ site.baseurl }}/docs/r/">R</a>, <a href="https://github.com/apache/arrow/blob/master/ruby/README.md">Ruby</a>, and <a href="https://docs.rs/crate/arrow/">Rust</a>.
+      <p>Libraries are available for <a href="{{ site.baseurl }}/docs/c_glib/">C</a>, <a href="{{ site.baseurl }}/docs/cpp/">C++</a>, <a href="https://github.com/apache/arrow/blob/main/csharp/README.md">C#</a>, <a href="https://godoc.org/github.com/apache/arrow/go/arrow">Go</a>, <a href="{{ site.baseurl }}/docs/java/">Java</a>, <a href="{{ site.baseurl }}/docs/js/">JavaScript</a>, <a href="https://arrow.juliadata.org/stable/">Julia</a>, <a href="https://github.com/apache/arrow/blob/main/matlab/README.md">MATLAB</a>, <a href="{{ site.baseurl }}/docs/python/">Python</a>, <a href="{{ site.baseurl }}/docs/r/">R</a>, <a href="https://github.com/apache/arrow/blob/main/ruby/README.md">Ruby</a>, and <a href="https://docs.rs/crate/arrow/">Rust</a>.
       See <a href="{{ site.baseurl }}/install/">how to install</a> and get started.
   </div>
   <div class="col-lg-4 mt-3">
diff --git a/install.md b/install.md
index 49fa406..42c5900 100644
--- a/install.md
+++ b/install.md
@@ -283,7 +283,7 @@
 [13]: {{site.data.versions['current'].asc}}
 [14]: {{site.data.versions['current'].sha256}}
 [15]: {{site.data.versions['current'].sha512}}
-[16]: https://github.com/msys2/MINGW-packages/tree/master/mingw-w64-arrow
+[16]: https://github.com/msys2/MINGW-packages/tree/HEAD/mingw-w64-arrow
 [17]: https://brew.sh/
 [18]: https://github.com/Microsoft/vcpkg
 [19]: {{ site.baseurl }}/release/
diff --git a/overview.md b/overview.md
index 241b7db..eb1a4c7 100644
--- a/overview.md
+++ b/overview.md
@@ -80,8 +80,8 @@
   <div class="col-md-12">
     <h3>Arrow Libraries</h3>
     <p>
-      The Arrow project contains libraries that enable you to work with data in the Arrow columnar format in many languages. The <a href="{{ site.baseurl }}/docs/cpp/">C++</a>, <a href="https://github.com/apache/arrow/blob/master/csharp/README.md">C#</a>, <a href="https://godoc.org/github.com/apache/arrow/go/arrow">Go</a>, <a href="{{ site.baseurl }}/docs/java/">Java</a>, <a href="{{ site.baseurl }}/docs/js/">JavaScript</a>, <a href="https://arrow.juliadata.org/stable/">Julia</a>, and <a href="https://docs.rs/crate/arrow/">Rust</a> libraries
-      contain distinct implementations of the Arrow format. These libraries are <a href="{{ site.baseurl }}/docs/status.html">integration-tested</a> against each other to ensure their fidelity to the format. In addition, Arrow libraries for <a href="{{ site.baseurl }}/docs/c_glib/">C (Glib)</a>, <a href="https://github.com/apache/arrow/blob/master/matlab/README.md">MATLAB</a>, <a href="{{ site.baseurl }}/docs/python/">Python</a>, <a href="{{ site.baseurl }}/docs/r/">R</a>, and <a href="https://github.com/apache/arrow/blob/master/ruby/README.md">Ruby</a> are built on top of the C++ library.
+      The Arrow project contains libraries that enable you to work with data in the Arrow columnar format in many languages. The <a href="{{ site.baseurl }}/docs/cpp/">C++</a>, <a href="https://github.com/apache/arrow/blob/main/csharp/README.md">C#</a>, <a href="https://godoc.org/github.com/apache/arrow/go/arrow">Go</a>, <a href="{{ site.baseurl }}/docs/java/">Java</a>, <a href="{{ site.baseurl }}/docs/js/">JavaScript</a>, <a href="https://arrow.juliadata.org/stable/">Julia</a>, and <a href="https://docs.rs/crate/arrow/">Rust</a> libraries
+      contain distinct implementations of the Arrow format. These libraries are <a href="{{ site.baseurl }}/docs/status.html">integration-tested</a> against each other to ensure their fidelity to the format. In addition, Arrow libraries for <a href="{{ site.baseurl }}/docs/c_glib/">C (Glib)</a>, <a href="https://github.com/apache/arrow/blob/main/matlab/README.md">MATLAB</a>, <a href="{{ site.baseurl }}/docs/python/">Python</a>, <a href="{{ site.baseurl }}/docs/r/">R</a>, and <a href="https://github.com/apache/arrow/blob/main/ruby/README.md">Ruby</a> are built on top of the C++ library.
     </p>
     <p>
       These official libraries enable third-party projects to work with Arrow
diff --git a/powered_by.md b/powered_by.md
index 01e76d1..ec36890 100644
--- a/powered_by.md
+++ b/powered_by.md
@@ -228,7 +228,7 @@
 [24]: https://github.com/Paradigm4/accelerated_io_tools
 [25]: https://github.com/uwdata/falcon
 [26]: https://fastdata.io/
-[27]: https://github.com/apache/arrow-site/edit/master/powered_by.md
+[27]: https://github.com/apache/arrow-site/edit/main/powered_by.md
 [28]: https://github.com/uber/petastorm
 [29]: https://www.inaccel.com/
 [30]: https://www.mathworks.com