This phrase means to continue doing something that you had stopped doing. This is useful for talking about work, lessons, games, or other things that continue for more than one day:
One thing I like about listening to audio books is that you can pause them and pick them back up later without searching for where you stopped.
I didn't speak English for a few years, but I was able to pick it back up with no problem.
Another related phrase is "pick up where (one) left off". This means to continue something from the same point that you stopped at last time:
OK, well it looks like time's up, but we'll pick back up where we left off tomorrow.