Offensive holding happens in American football when an offensive lineman holds a rushing defensive player.

"But that happens all the time!"
Kinda. The actual definition of "holding" here should be read as "clamping onto an opposing player to limit his movement." While linemen are allowed to use their hands, they may not simply latch on to an arm or jersey. Technically, they also may not tackle an opposing player who has otherwise slipped by them.

Can I Get Your Number?
I know that still sounds vague, so here's the generally accepted rule. If an offensive lineman keeps his hand(s) inside the opponents shoulder and chest area, on the jersey number, he may grab and hold the opponent as long as he keeps the defender in front of him. This way, the offensive lineman keeps his hands on the "inside" of the defender. If an offensive lineman reaches around to the "outside" of a player (think bear hug), a flag and whistle are sure to follow.

Play Fare
In college, the penalty is ten yards from the spot of the foul. In professional football, the penalty is ten yards from the line of scrimmage.
You get a bonus two points if you understand the pun in this paragraph heading instead of /msg me about a typo.