The pockets in a pool table get worn out after a while. If you make a shot and your ball plops in the pocket and rolls out onto the floor, then your pockets are worn out. If you replace the felt on your table, you also should replace the pockets so the pool table looks fresh all over.
Unscrew the bolt underneath the table at each pocket and remove the plate that holds the pocket in place. If you have bolted on pockets, then you may need custom pockets to replace these ones, since they are not as ubiquitous as modern cloth and tubular pockets.
Pop off the cover that holds the pocket in place and remove the old pocket. You can purchase new pockets for these types of tables in sets of six if you are planning to replace all of them, or use the old pockets as a pattern to cut and sew new ones.
Use rivets or a heavy strip of cloth to attach new netting to worn pockets if you don't want to remove the entire piece. If you just sew on new netting, it can easily unravel and fray, requiring you to replace it again sooner than later.
Redo your entire pool table with a new rail system that has the pockets built in to the rails. These pockets will typically utilize cups to catch the balls or sliding tube systems. Cups can easily be replaced by lifting them out, and they are easy to clean and inexpensive to replace. You can spiff up your felt and add good hard bumpers for better play if you take the time to give your whole table an overhaul after heavy use and wear.