a (somewhere)-bound local train

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.

There is no service between (somewhere) and (somewhere)

When a train line is not running as usual, you will see signs or hear announcements saying that "There is no service between ___ and ___." This means that the train doesn't stop between those two places.

Another example of "no service" is on a telephone that doesn't work. If you try to call someone but nothing happens, you can say:

There's no service.

34th Street and Canal

When people name two streets one after another, they often don't say "street" after the second one:

It's on the corner of 15th Street and Lexington.

You can actually skip the word "Street" on the first one too in casual English:

It's on the corner of 15th and Lexington.