What makes sets faster than lists?

list: Imagine you are looking for your socks in your closet, but you don't know in which drawer your socks are, so you have to search drawer by drawer until you find them (or maybe you never do). That's what we call O(n), because in the worst scenario, you will look in all your drawers (where n is the number of drawers).

set: Now, imagine you're still looking for your socks in your closet, but now you know in which drawer your socks are, say in the 3rd drawer. So, you will just search in the 3rd drawer, instead of searching in all drawers. That's what we call O(1), because in the worst scenario you will look in just one drawer.

Sets are implemented using hash tables. Whenever you add an object to a set, the position within the memory of the set object is determined using the hash of the object to be added. When testing for membership, all that needs to be done is basically to look if the object is at the position determined by its hash, so the speed of this operation does not depend on the size of the set. For lists, in contrast, the whole list needs to be searched, which will become slower as the list grows.

This is also the reason that sets do not preserve the order of the objects you add.

Note that sets aren't faster than lists in general -- membership test is faster for sets, and so is removing an element. As long as you don't need these operations, lists are often faster.