If you are just looking for a broad overview then your best bet is to simply view the changelog.txt file. If you want to do this without downloading the newest version then simply go the main git page (for us it would be https://github.com/CleverRaven/Cataclysm-DDA) and then go to the data/changelog.txt file. (Be warned that the changelog only tends to update about once a week or so during development, however).
If you want a more in-depth view then there are two different ways to view the differences:
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Go to the github repository site you would like to compare, and then click the green “Compare and Review” button (it looks like two interlocking arrows). Then for your branches you can set time limits, for example to see everything that has happened in the last day you would use “master” and “master@{1.day.ago}” (you can also do things like months here as well). If you go back to the main page and click on “releases” then it will also tell you how long ago the various releases were.
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Alternatively you can view the entire changelog by simply clicking on the “commits” link from the main page, though this starts you at the most recent changes and works its way backwards.