Next to the left offensive tackle, offensive center is the most important position on the offensive line to fill.
Many offensive centers at the high school level are the most athletic and undersized guys on the offensive front. Today's offensive center is often uncovered at the line of scrimmage with so many teams playing 4-3 defenses at the college level, so athleticism is a plus.
Much of the time they must be able to reach the linebacker, adjust to the moving target and block in space. They have to have feet and must be proficient in angle blocks and also have the range to help out pass pro. In some cases, they may even have to pick up an outside pass rusher.
However, there is another factor that must be considered. As much as teams are looking for an athletic, "position"-type offensive center, if the players do not have enough strength and bulk to anchor at the point of attack, defenses will find them and put a big defensive tackle on their nose or play a 3-4 scheme. This can create a mismatch and totally disrupt the run game.
While athletic ability and feet are very important, size and strength cannot be ignored. This is why so many kids make the move from offensive tackle in high school to center at the college level.
The other quality important for any offensive center is intelligence and football instincts. In many cases, they make the offensive line calls and have to anticipate, recognize and react quickly.