If you are competent, you have the necessary ability or skills to do something. If you can carry a heavy tray of food and store a table's worth of orders in your head, you are probably a competent waiter.
The opposite of competent is incompetent — an incompetent travel agent might send you to Bahrain when you requested Britain. But competent on its own can sometimes be a veiled criticism, with the implication that someone competent is just going to through the motions — you'd rather have someone inspired on the job. In legal language, competent describes someone who has the mental capacity to take part in a trial or sign a contract.