What does git --set-upstream do?

I tried to understand it by reading the git manual, but I didn't quite get it.

To avoid confusion,
recent versions of git deprecate this somewhat ambiguous --set-upstream option
in favor of a more verbose --set-upstream-to option
with identical syntax and behavior.
[ Reference ]

git branch --set-upstream-to <remote-branch>

sets the default remote branch for the current local branch.

Any future git pull command (with the current local branch checked-out),
will attempt to bring in commits from the <remote-branch> into the current local branch.

One way to avoid having to explicitly type --set-upstream / --set-upstream-to is to use its shorthand flag -u as follows:

git push -u origin local-branch

This sets the upstream association for any future push/pull attempts automatically.
For more details, check out this detailed explanation about upstream branches and tracking.