Important, but not important.
The strange thing is that I found Desmond's story and Altair's story as the reason to keep playing, not Ezio's. Ezio's story is nothing special and basically involves looking for 5 discs that unlock Altairs memory and with all 5 he can enter Altair's vault. Every time you get an Altair disc you get to play a memory involving him. The first takes place before the first game, but the others all take place after Assassin's Creed 1 and go all the way until he dies of old age which is really cool.
For Desmond's story he is still in a coma and cannot awaken until he finishes living Ezio's memories and triggers a Nexus sync. Instead of leaving the Animus like you can in past games this time when you quit Ezio's memories you go to Animus Island. Here you interact with subject 16 as he gives you information. Also every time you collect so many data fragments you can access these parts about Desmond's early memories. Basically you go into these platform type rooms and it is in first person. It is not very fun, but it is cool to hear Desmond speak about his early life as an Assassin. Another part of Desmond story is every time you finish an important mission or sequence and the game is loading you hear Shawn, Rebecca, and a new guy named William talking. You hear them talking about Desmond and some other things which was interesting to me.
In terms if the first civilization story line most of it comes in towards the end. You get a little with Altair, but a lot is in the ending. The ending greatly deals with information about the first civilization.
Game play wise it is more of the same. There is a new thing called a hook blade which is cool and allows you to reach further ledges while jumping. There is a tower defense mini game that is kind of fun which you use to defend towers in this game.