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:

New York-bound local train, now boarding on track three.