Frequency Response is a measure of if your cans can play from very low notes to very high notes all at the same loudness. The most important thing in those graphs is that they are flat, meaning even. The next most important thing is where the bass response drops off. Lower is better.

It is true for all speakers and headphones, but it is not as straight forward for headphones because everyone's ear is shaped different thus will mess with the FR. Good headphones are flat and go down to at least 30Hz. Lower is better.

Depending on your player, you may use Digital Signal Processing to help flatten things out. Its complicated, but the results can be fantastic.

I don't think it's been mentioned yet, but open vs closed is an important consideration. Open tend to be better IMHO but only if you listen in a closed controlled environment. If you are surrounded by noise, closed backed headphone are better because what little you gain in playback fidelity is dwarfed by cutting out the noise of kids playing, the kitchen fan running while dad cooks and people talking on the subway. Good sound isolation is heaven when needed, but also slightly impacts bass response. I have both and use the right one for the environment.