Grip strength is paramount in the grappling aspect of MMA. All of the best ground fighters are said to have an iron grip, which allows them to control their opponent's limbs on the ground and eventually secure the submission. Typically, grip strength will develop over time with consistent grappling and working of the muscles. There are also several workouts you can do to help promote grip strength.
Most of the power in your grip comes from the forearm. There are numerous muscles in the forearm, including groups of flexors and extensors. You'll want to work on the former, since these are the ones that help aid grip strength. Forearms require high volume to really shine, so be sure to work them at least two or three times a week. Note that you do not have to isolate them every time, as many heavy lifts will really work the forearms.
The two best traditional exercises with which you can increase your grip strength are the deadlift and pull-up. Deadlifts are arguably more better than pull-ups, which is why many lifts will use straps to help them support the weight. Since you're trying to promote grip strength, you can forego the use of straps, although gloves and chalk can be used. You can also use the chin-up variation of the pull-up, which will put additional stress on the wrist flexors. Another good exercise to consider is the dispute, which also uses a large amount of weight to facilitate grip strength.
While your grip can be increased with traditional exercises, there are a few that will isolate the forearm. If you have any wrist injury, you should be careful of some of these exercises, as they require significant rolling of the joint and can cause uneven stress, which can lead to pain. The one I like to use the most is the standing barbell wrist curl, which is where you place a barbell behind your back and curl it up with your wrists. This is a good exercise that will greatly increase grip strength without really placing the joint in a compromising position. You can also try dumbbell wrist curls, but I find these to be too uneven, which can lead to pain. I had a ganglion cyst in my wrist for a while, and these would really make it hurt!
As I mentioned above, your grip will increase in strength with time, but you'll need to exercise your forearms to really gain elite strength. In grappling, this is important because it allows you to control your opponent and tie him up if he's ontop of you.