Your character accumulates "edge points" by doing various things. The main one is getting imm-awarded xp, but I think you can also get some for advancing in rank and/or hours-played.
If you have enough "points" to take an edge *AND* meet that edge's prerequisites then it will be displayed in your list. There may be other edges that aren't displayed because you don't meet the prerequisites, even if you would otherwise have enough "points" to take them.
Prereqs can be lots of things. % in a skill is a common one, esp. for edges that augment a particular skill. # PK wins, # PK losses and Gank-o-meter also play a part in certain edges, I suspect. Some edges are only available to races that are sufficiently strong, intelligent, wise, dexterous, etc. For instance, there were some shaman edges that were off-limits to my duergar.
