Whats the difference between all the different cousins?

I know what 1st cousins are, but who would be 2nd and 3rd cousins? What does the once, twice removed mean?

What would my dads 1st cousins be to me? What about the kids of my dads 1st cousins, what would they be to me and my dad?

A system of degrees and removes is used to describe the relationship between the two cousins and the ancestor they have in common. The degree (first, second, third cousin, etc.) indicates the minimum number of generations between either cousin and the nearest common ancestor; the remove (once removed, twice removed, etc.) indicates the number of generations, if any, separating the two cousins from each other.

For example, a person with whom you share a grandparent is your first cousin; someone with whom you share a great-grandparent is a second cousin. Where your relationship to the nearest common ancestor is different from your cousin's relationship then the term "removed" is used to indicate this, for example the child of your first cousin is your first cousin once removed because there is a generation between you.