If it's a conflict due to a rebase, you could always imagine like so -
Your master branch is fixed
A feature branch that originated from an older commit on master, is shifting itself from there to the latest commit on master (that's what a rebase is, at its core).
Now, if you see from the point of view of master -
incoming changes are the ones that move to master (i.e. changes in your feature branch), hence the term.
current changes are the ones that are already present in master (i.e. ones done by fellow developers or yourself on master).
In case of merge conflicts, as suggested by @VonC, the terminology is reversed.