What does the phrase 1 meter per second mean?

Answer 1

It's a measure of acceleration. It means something is gaining 1 m/s of speed every second it accelerates.

Answer 2

1 m/s/s is an increase of speed (acceleration) of 1 m/s per second, that is, if something has acceleration 1m/s/s, it speeds up by 1 m/s each second.

Answer 3

That means that whatever is moving is moving 1 meter every second that goes by.