Definition of 3 barrel
A 3-barrel is when a player who has the preflop lead (the player who made the most aggressive action preflop, probably a raise) will bet on the flop, turn and river. The 3-barrel can be a value bet because you have the nuts and want to get paid or a bluff. This is called a 3-barrel bluff and is a great tool for aggressive play. You can make a 3 barrel whether you are in position or not, the important thing is to have the lead.
A 3 barrel in practice
Let's take the example of a 3 barrel bluff. The player on the button opens preflop when the players before him have all folded. He has an ace and a queen in spades. The player in the small blind (SB) calls the bet and the big blind folds. The flop comes 8-9-J with 2 spades. This is an excellent flop for the original raiser (button). The player in the small blind who first calls on the flop decides to check. The player in button position bets (1st barrel). The SB calls. The turn is a brick, say a 2 of hearts. SB checks and button bets (2nd barrel). Finally, the river is a brick, say a 2 of clubs and button decides to go all in by betting his 3rd barrel, hoping to get the small blind to fold.