Don't you know the train keeps a-rolling?

from Arctic Monkeys – Stop the World I Wanna Get Off With You Lyrics on Rap Genius

Meaning

Trains are very hard to stop. Alex and this woman are two people who don’t stay in one place for long and once they start moving they’re hard to stop.

Trains specifically are a possible reference to Johnny Cash who popularized the metaphor for saying that life goes on and doesn’t stop for thinking too much and possibly regretting it later.

To help improve the meaning of these lyrics, visit “Stop the World I Wanna Get Off With You” by Arctic Monkeys Lyrics and leave a comment on the lyrics box