Definition of bet sizing
Literally "bet sizing". A bet sizing is the ratio of a bet to the size of a pot. For example, on the flop, let's say the pot is $10. If you play online, your poker room will probably have shortcut buttons for different bet sizing. These buttons will be labeled 1/2, 3/4 and POT. You may also have other options like 1/4. These options are different bet sizing.
Involvement of bet sizing
Bet sizing in poker is an art form. Every time you bet, you'll study your bet sizing. If your opponent is passive and you have a very strong hand, you will want to use a small bet sizing to get him to call your bet. On the other hand, depending on his level of thinking, a small bet sizing may give the impression that you are looking for a call with a very strong hand, which could encourage him to fold. You might then recommend a very large bet (bet pot) to make him think that you are trying to bluff him. And if you're up against a player who hates to be bluffed, you may want to choose a huge bet sizing to maximize the money you make from your hand.