The right grip size makes a huge difference in how a racquet performs. The average size for a male is a 4-3/8 and the average for a female is a 4-1/4. If you feel you have bigger hands than the average, then you should go one grip size larger. If you are unsure, choose the smaller size. You can always make a grip bigger but you can't make it smaller! To make a grip bigger you can simply add an overgrip (this increases the grip size 1/16 or half a grip size). You can also get your local pro shop to add a "heat shrink sleeve" which increases the grip by 1 full size.
If you're not sure of your grip size, here's a simple way to measure:
Holding an eastern forehand grip (the palm is placed against the same bevel as the string face), you should be able to fit the index finger of your non-hitting hand in the space between your fingers and your palm.
If there isn't enough room for your index finger, the grip is too small. If there is space between your fingers and palm, the grip is too big.
A grip that is too small requires more muscle strength to keep the racquet from twisting in your hand. Prolonged use of a grip that's too small can contribute to tennis elbow problems. A grip that's too large inhibits wrist snap on serves, makes changing grips more difficult and also requires more muscle strength. Prolonged use of a grip that's too big can also contribute to tennis elbow problems.