There are hundreds of different mountain bike tyre designs available. Choosing the right one for your riding is a real challenge, so here's the essential knowledge...
Speed vs. Grip
Tread design is inevitably a trade-off between rolling speed and grip. The toothier and wider-spaced the tread, the better it'll bite into the ground but the slower it'll roll. Using a softer compound will add even more grip, but slow you down even further. Therefore, you have to decide whether you want maximum straight-line speed but a tyre that needs nursing round corners, or a slower tyre that can be pushed harder in technical situations.
Dry vs. Wet
The trouble with many fast tyres is that they're designed to work on dry, dusty or gravelly desert terrain. Unfortunately, these small, closely spaced designs clog quickly in damp, sticky conditions. Continual centreline tread patterns also slip and slide really badly on the polished, wet roots that come out to play on the early morning laps of UK 24-hour races. On the other hand, broader, flatter, wider-spaced tread patterns (Racing Ralph, Razer MX, Speed King) clear quickly and cope well in wet and dirty conditions (on the back at least).
Survival vs. Speed
The lightest, skinniest tyres are the fastest around, but whatever time you make up in rolling speed you'll lose several times over if you puncture them. Big, heavy-duty, reinforced downhill/freeride tyres make you feel invincible, but if you ride them uphill they'll kill you. The new breed of 2.3in tyres offer a great balance of performance. The extra weight makes acceleration a bit harder but the tread patterns mean low rolling resistance. They also have a large footprint for confident grip and enough air in them to smack through stuff without worrying. This means you can take aggressive lines through technical sections and maintain a higher overall speed than a theoretically faster, lighter tyre.
Mix 'n' Match
Finally, don't assume the same tyre - or even brand - front and back is the best solution. The front tyre is much more important for braking and cornering grip, while the rear has a greater effect on rolling speed. A grippy front tyre and a slick rear can often be the best combination.