To "pick something back up" is to re-learn something or to restart something "I haven't spoken German for a long time, but I'm sure I could pick it back up again". "Pick up where I left off" - restart something at the point where I stopped. "to pick back up" - Get busy after a slowing down "Business is slow this afternoon, but it should pick back up again tonight." "to pick up" - get busy. "The economy is picking up recently."

When you drop something, you pick it back up. pick it back up = pick something up after dropping it