In the sport of boxing, the clinch is used for one basic reason.
The main reason boxers clinch is to break the other fighter's momentum. When a boxer is on the offensive, his opponent may cover up in an effort to avoid getting hit. If the advancing boxer continues to strike his opponent, he will certainly inflict a fair amount of damage and the defending fighter may not be able to counter strike. The striker is now in control and the fight could take a nasty turn unless the fighter being beaten can change the momentum in his favor.
A common tactic that boxers employ is the clinch position. By stepping forward and throwing his arms around his opponent, the attack will stop momentarily. While in the boxing clinch, the defender leans into his opponent and lays his weight into him. It is very difficult for either fighter to throw an effective boxing punch while in the clinch and fight fans typically do not appreciate the tactic because it's not very exciting to watch.
The referee won't let fighters clinch for long, but there's really not much he can do other than break the fighters apart. Excessive clinching may earn points deductions after a few warnings, but this is a rare event.