Contact is a measure of how well a player can hit when the bat does not hit the 'Sweet Spot'.
When a player swings, the bat's position relative to the ball is measured. If the ball does not come close enough to the fat part of the bat, the contact rating is subtracted from the hit power for that particular swing. A home run may still be hit, but it is much more difficult. For this reason, low contact ratings are better than higher ones. Wade Boggs has a low rating of 4, while Marc Sullivan, Rafael Santana, and Jim Lindeman all have the highest (and worst) position player rating of 38. Pitchers have a contact rating of 64.
For more details on the technical side, see Contact Explained