git stash push -p -m "my commit message"

-p let's you select the hunks that should be stashed; whole files can be selected as well.

You'll be prompted with a few actions for each hunk:

y - stash this hunk

n - do not stash this hunk

q - quit; do not stash this hunk or any of the remaining ones

a - stash this hunk and all later hunks in the file

d - do not stash this hunk or any of the later hunks in the file

g - select a hunk to go to

/ - search for a hunk matching the given regex

j - leave this hunk undecided, see next undecided hunk

J - leave this hunk undecided, see next hunk

k - leave this hunk undecided, see previous undecided hunk

K - leave this hunk undecided, see previous hunk

s - split the current hunk into smaller hunks

e - manually edit the current hunk

? - print help