what's the purpose of the puzzle?

sometimes it seems the goal is checkmate and sometimes taking advantageous position, .... etc.

I'm confused 

Puzzles are designed so you will find patterns in positions and correlate them with your real games. One simple example would be the back rank mate. And as you grow more advanced it will build on to maybe sacrifing your queen because you have a back rank mate. The same thing applies with gaining an advantageous position. The "base" tactic might be taking a free piece and as you grow stronger it is trading a piece because you can then fork a king and rook. The point being that over time these ideas/patterns will become easier to spot thus improving your tactical game.

That's part of what it is asking you to figure out. They're implying there's an opportunity of some sort by the puzzle existing, but it's up to you to work out the specifics and catch exactly what is going on.