A tileset is a group of tiles you put on a piece of gear. Every tile is an action. Like a fireball or haven’t hit a monster for over 2 seconds.
When you execute those actions in the order of your tileset than the tileset will trigger. This triggered tileset stays for a few seconds (4 to 8 seconds depending on length of the tileset) and gives you a damage boost of a bit less than 10% (the logic of the boost itself is a whole can of worms on itself I won’t bother you with now). You can keep up 3 tilesets at a time. If another procs it just overrides one of the 3 that are already active.
Tilesets can be used in every class. They all have their own specific tilesets.