Among the zillion different brands, types, and sizes of tires there are three styles: symmetrical, asymmetrical, and directional.
Symmetrical tires are the most common and have the same tread pattern from one side to the other; it doesn’t matter which side is mounted out.
Asymmetrical tires are designed to have one side mounted toward the outside of the vehicle. The outside of the tire typically has larger, tighter tread blocks to improve tire wear, handling, and dry traction while toward the inside of the tire the tread blocks are smaller and more spread out and contain more sipes (small cuts in the tire tread to improve wet traction). I thought these were kind of interesting because I’ve never seen a tire designed to be mounted differently depending on whether it would be used in a dry or wet climate. I guess Los Angeles mounts them one way and Seattle mounts them another?
Directional tires are designed to be rotate in one direction only and typically shed water better.
For a more in depth description you can check out Tire Rack or do a little Googling if you’re looking for a new set of tires.