Let's say you are working on feature branch F, but you notice that origin/master M has been updated with commits that you want to merge onto your feature branch.
The synchronize function does this in a sensible manner.
Going from:
--*--*--*--*(M)
\--*(F)
to:
--*--*--*--*--*(F)
This allows for a cleaner history than manually fast-forwarding the master branch onto your feature.