Tires - tread types
Cutaway tire.
Cutaway tire.
Cutaway tread
Cutaway: Cutaway tread gets its name because it appears that the low sections have been "cut away" from thicker areas. There are channels between wide flat areas of tread. In general, cutaway treads roll very smoothly on pavement or smooth rock, because the surface "sees" a continuous flat surface. The tread becomes active when the tire encounters loose or wet trail. Cutaways are often bi-directional -- the tread is the same either direction. The tire above, if placed on a rear wheel, wound be mounted so the "pointy" part of the tread aims in the direction of travel (when viewed from the bottom of the bike). The flat ends would "push off" as the tire drives the bike.
Knobby tire.
Knobby tire.
Knobby tread
Knobby: Knobby tires have bumps that stick up from the surface. These tires are excellent in loose or damp terrain. Knobbies make more noise, and have a rougher ride, but the payoff is better hold on the trail. This tire is mounted on the front. Because the front tire's job is to STOP the bike, the wide (higher) side of the center knobs aims towards the front of the bike, when viewed from below. This gives the tread better holding power. If this tire were mounted on the rear, it would be reversed -- the wide "trail-grabbing" side of the knobs would face the rear of the bike as the tire meets the trail. Widely spaced knobs are better in mud and snow. Most racing tires are knobby tires with smaller knobs. The UMB on-line store sells high-performance and XC race tires.  
Bar tread tire
Bar tread tire
Bar tread
Bar: Bar tires are used only on the rear wheel. The transverse bars "scoop" loose dirt, mud, and snow to drive the bike forward. A bar tire is very rough and noisy on pavement. Because the tread is uninterrupted through the center of the tire, this tire has less lateral (side-to-side) hold than a knobby -- the wheel will be more likely to side-slip when traversing a rock slope or when turning on a loose trail.
Semi-slick tire
Semi-slick tire
Semi-slick tread
Semislick: The semislick tire has a band of smooth tread in the center of the tire. This makes the tire roll very smoothly on pavement or stone. These tires are often referred to as "commuter tires" because they offer very little rolling resistance when you ride them on pavement. On the sides of the tire, aggressive knobs hold when the bike leans. Semislick tires can be good on hard-pack trail or sandstone. Because there's less rolling resistance, and the weight of the tread is reduced, these can be good racing tires if the course doesn't include much loose stuff.