Essentially an all-season tire is a tire with a slightly aggressive tread pattern that provides good year-round wet and dry traction characteristics. It tends to be a bit harsher and louder than ordinary tires, but not as harsh or loud as a snow tire.
Some all-season as well as performance tires have a "directional" tread pattern. Directional tires have a "one-way" tread pattern that are optimized for the direction the tires rotate on the car. They must therefore be mounted on either the left or right side. Little arrows or triangles on the sidewall indicate which way the tire is supposed to turn. The tread blocks and grooves are angled to optimize handling. They also do a good job of channeling water out from under the tire on wet surfaces to reduce hydroplaning and improve wet traction. Directional tires can be rotated front-to-rear but cannot be rotated side-to-side.
Another variation in tread design you'll see is "asymmetrical" tires. Tires with an asymmetrical design mix tread patterns or put more rubber on one side of the tread than the other in an effort to make one tire out of two different tread patterns. Some combine a slick-like smooth tread on half the tire (to improve traction) with a block pattern on the other half (for directional stability).