Definition of continuation bet
A continuation bet is a bet that a player makes when he has the initiative. To have the initiative, you must have made the most aggressive play on the previous street. For example, a player limp before the flop, I isolate him by raising to 5 big blind and he calls. I have the initiative. If I decide to bet on the flop, it will be called a continuation bet. If my opponent calls and I bet on the turn, it will be called a continuation bet on the turn. A continuation bet on the turn necessarily implies that a continuation bet has been made on flop. If I don't bet on the flopth and I bet on the turn and I have the initiative, then it will be said that I made a "delayed continuation bet" so a delayed continuation bet.
History of the term
Dan Harrington is credited with coining the term, which he theorized in his tournament trilogy. The term is now widely used. The trackers like Poker tracker 4 and Xeester also use it in their statistics. A continuation bet is not a standard bet. If you analyze your opponents, you will notice that they have a continuation bet higher than their general betting frequency.