In order to unlock any tier in a given skill tree you have to have five skill points multiplied by the highest tier have already opened applied in that tree.
So you have three trees. Put five skill points into one tree's first tier and you open the second tier of that one tree, but not the other two. If you put a total of ten points into any of the skills in the first two tiers the third tier opens. 15 for fourth tier, etc. The point is to focus your skills in one of the three trees. There are some "hybrid" skill sets out there, but they are not important to new players.
If you go to http://www.torhead.com/skill-calc
you can build different skill sets and you can see what I mean without having to level a character.