Grips

In drumming, there are two ways to grip the sticks: traditional and matched.
The Traditional Grip
It is also known as the Orthodox grip. Your hands hold the sticks differently. The right hand uses an overhand grip while the left hand uses an underhand grip. The stick on the left hand is placed between the drummer's left thumb and forefinger. Why is it called traditional? because it descends from military marching drummers who carried a snare drum on a sling hung from the neck or one shoulder, with the drum riding closer to one hip than the other and tilted slightly for easier reach. Jazz drummers enjoy this grip because they are required  to play a great deal of intricate rhythms with a soft touch.
The Matched Grip

L-R: Matched Grip, Traditional Grip

Here is the opposite of the traditional grip as your hands hold the sticks in the same way. Both hands use an overhand grip. The matched grip is performed by placing the stick between your thumb and forefinger and grasping or pinching the stick. This is the grip used by almost all drummers.