if you are going to pay attention to the story it most definitely does. but if your one of those people who just wants to "be kewl" and kill stuff then you probably won't have the attention span to finish it. i highly recommend playing it (rent it, you'll beat it in a weekend).
For the past (meaning Ezio's storyline), almost nothing. For the present (which is the MAIN storyline), you do. Just read a summary online, i.e. the assassins creed wiki - http://assassinscreed.wikia.com/wiki/Assassin%27s_Creed#Plot
Main thing is that the present storyline is basically sci-fi, and that element is present in Altair's and Ezio's storyline, so it is necessary to know the plot before playing AC2, seeing as the ending is quite 'out there' for all the AC games.
Actually there are some things you need to be aware of, although the development of these storylines occurs mainly in AC2 and beyond.
Basic: There are objects of power called Pieces of Eden, which a company called Abstergo (formerly the Templars) seek to collect. They've constructed Animus' which allow people to relive the memories of their ancestors, and Abstergo forces certain people with the right bloodline to use these machines in order for them to discover the locations of these ancient POE's. Most of these people are within the "Assassin" bloodline, the origin of which you will learn more about in AC2.
Less basic: Prolonged Animus use causes "bleeding" wherein a subject will begin to experience these memories outside of the Animus and lose touch with reality. A certain subject who is very important to Abstergo for reasons we don't yet quite know, "Subject 16", was so affected that he went insane, but also was able to hack the Animus and is planting clues inside for us to find while we play as Ezio so we can stop Abstergo...but also so that we can stop some major disaster that is going to happen to Earth.
Most hidden: Via hidden emails you can intercept and a few other things, we've discovered that Abstergo plans to use the PoE's in a scheme where they launch them into space inside satellites, and use their presence to control the human race.
Playing through the first one doesn't take that long if you only do the bare minimum of intel gathering to get through your list of missions to complete the game. As has been said, its a bit repetitive but the story is great. Your master in the game is done by the voice actor who did Duncan in Dragon Age and the whole assassin/master dialogs are great. I actually like the swordplay in AC1 a little more than the newer games.