A "local" train is one that stops at every station that's listed.
The opposite of a "local" train is an "express" train, which skips some stops in order to take passengers to far-away areas more quickly.
The phrase "___-bound" describes where the train is going to.
You can use "local train" and "___-bound separately:
I need to take the local train.
Is this the local?
Which one is the New Jersey-bound train?
Train announcers announce both in the same sentence: