Originally posted by Malnaur:

To be slightly more detailed, dedicated servers suspend when no one is logged in so no time passes at all. Plus is no raids or other mishaps, minus is no progress for crops etc.

Isn't that the same as a local save? In both cases time stops if no one is in the world.

The only real difference is that someone else might log in, which will cause time to pass, so the crops will see that time advancement when you enter the area, similar to if you enter an area after doing something somewhere else.