The possession arrow is one of several rules that differentiates college basketball from professional.
Officially know as the alternating-possession procedure, it is defined in the NCAA rulebook as "a method of putting the ball in play with a throw-in rather than a jump ball."
This rule comes into play during an alternating-possession situation, which can include: a held ball, a free-throw violation or technical foul when no team is in control, and a live ball becoming wedged between the backboard and the rim.
Here's how it works.
Every NCAA basketball game starts with a jump ball at center court.
The possession arrow remains off until one team attains possession of the ball after tipoff. Once that happens, it's turned on and points in the direction of the team that lost the opening tip. Let's call them Team 1. They'll be given the ball when the next alternating-possession situation happens.
Team 1 then successfully inbounds the ball after said situation occurs, and the arrow is reversed to point to the other team, Team 2.
But the arrow will also be reversed if any player touches and causes the ball to go out of bounds, or if the thrown-in team (in this case Team 1) commits a throw-in violation. (If Team 1 commits that violation, they lose the opportunity to make the alternating-possession throw-in.)
However, any foul committed by either team during a thrown-in attempt will not result in the reversal of the possession arrow.
The same procedure will be repeated for every alternating-possession situation.
In short, the team that the possession arrow is pointing toward will always get the ball in these situations. The arrow is reversed after this procedure is complete, thus pointing to the team that didn't get the ball. They will then have possession in the next situation.
The direction of the arrow will be changed prior to the start of the second half to "account for the teams switching ends of the court." This ensures that the team that had it at the end of the first half will still have it to begin the second.
Finally, let's say that Team 1 and Team 2 are going to overtime. The possession arrow is reset, and (since overtime begins with a jump ball) adheres to same format it did to start the game.
If additional overtime periods are needed, the arrow will also be reset after the initial jump ball.