A 3-bet is a re-raise, meaning there is a bet, a raise, and then a re-raise. You'll hear and read about 3-betting before the flop mostly, since it becomes so common preflop. Preflop you count the big blind as a bet, so that's why we say you can call or raise preflop, meaning raise the big blind. Then a 3-bet is re-raising that bet. A 4-bet is just re-raising that bet, and it continues on and on but usually you only see 3-betting, sometimes 4-betting.
Double barreling is a term used when you have raised preflop and bet the flop and bet the turn. A triple barrel bets the river as well.
Check-raising is when you check with the intention of letting one or more opponents bet and then raising this bet.
That's the basic idea behind your questions. Now you know what the terms mean, you can begin the much longer and harder process of learning the theory behind them.