Now that you have changes from other people in the remote-tracking branches (or in the series of e-mails), you need to combine them, perhaps also with your changes. Or perhaps, your work on a new feature, created and performed on a separate topic branch, is now ready to be included in the long-lived development branch, and made available to other people. Maybe you have created a bugfix and want to include it in all the long-lived graduation branches. In short, you want to join two divergent lines of development, to combine them together.
Git provides a few different methods of combining changes and variations of these methods. One of these methods is a merge operation, joining two lines of development with a two-parent commit. Another way to copy introduced work from one branch to another is via cherry-picking, which is creating a new commit with the same changeset on another line of development (this is sometimes necessary to use). Or, you can reapply changes...