A URL of the form https://github.com/<owner>/<project>/commit/<hash> will show you the changes introduced in that commit. For example here’s a recent bugfix I made to one of my projects on GitHub:
https://github.com/jerith666/git-graph/commit/35e32b6a00dec02ae7d7c45c6b7106779a124685
You can also shorten the hash to any unique prefix, like so:
https://github.com/jerith666/git-graph/commit/35e32b
I know you just asked about GitHub, but for completeness: If you have the repository checked out, from the command line, you can achieve basically the same thing with either of these commands (unique prefixes work here too):
git show 35e32b6a00dec02ae7d7c45c6b7106779a124685
git log -p -1 35e32b6a00dec02ae7d7c45c6b7106779a124685
Note: If you shorten the commit hash too far, the command line gives you a helpful disambiguation message, but GitHub will just return a 404.