Position and flank experience indicates how well a player can play on a specific position (defender, midfield, forward or goalkeeper) or a specific flank (left, center, right). These values only change when playing matches.
Position experience gives a small bonus to tactics, scoring, dueling, blocking and passing. The maximum value for position experience a player can get from playing matches is 1000 (higher values can be reached but only with positional training in the training center), which would give a bonus of 0.75 balls on all the mentioned features.
Position experience is gained by playing on that specific position. When a player plays a match as defender his defender experience will increase, etc. When a player is not playing on that position (or not playing at all), his experience will slowly decrease. The higher the experience, the faster it will decrease. This makes it increasingly harder to gain more experience.
Some positions, like defensive midfielder, contribute to two positions. A player playing as defensive midfielder can use either his defender experience or his midfielder experience, whichever is higher.
Flank experience works in similar way but it is about 3 times less important than position experience. If you have to chose between a right defender and a left midfielder for the position of left back then it's much better to use the defender.
There is no actual "center" experience, when a player plays as center, he gets the average of his left and right experience bonus. He also contributes to both the left and right experience. This means a center player will play well on either flank too.