Don't quote me on any of this, but from watching pro play for a while I have a general understanding.
There are challenger team matches, where registered groups of challenger players from around the world will compete, and usually the winning team gets to replace a professional team (the one they replace usually places last in the LCS, which I'll get to). This is broadcasted, so it's actually like a full event.
They there is the LCS (League Championship Series). Each server (NA, EUW, KR, etc) has their own series, and during this competition professional teams will play against eachother in order to determine the qualifiers for worlds (which is why there are many NA teams, but you only see 2-3 in worlds).
After that, worlds.