Here's a breakdown:

* Arcseconds: A unit of angular measurement, where 1 arcsecond is equal to 1/3600th of a degree.

* Year: The time frame over which the angular change is measured.

So, a star with a proper motion of 1 arcsecond per year will appear to move 1 arcsecond across the sky each year.

It's important to note that:

* Proper motion refers to the apparent motion of an object across the sky, not its motion towards or away from us. That's measured by radial velocity.

* Proper motion is a very small effect, especially for distant stars. Even with a large proper motion, it can take many years for a star to move a noticeable distance across the sky.