I have Mass Effect 2, do I have to play Mass Effect 1 to understand the story?
I never played any of the games of Mass Effect series. Now I have Mass Effect 2, due to a promotion by Origin, in my library.
Is it possible to understand the storyline of the franchise without playing Mass Effect 1?
If you mean to ask: Do I need to play Mass Effect 1 to enjoy or understand Mass Effect 2?
Although the entire franchise is enjoyable - No. You do not "need" to play ME1 to understand or otherwise enjoy ME2.
Mass Effect 2 has a preface that brings players "up to speed" so they have all the pertinent information to fully understand what has happened and what is happening. It also allows players to make choices regarding events in Mass Effect 1 so that you're not stuck in a different story than someone who played Mass Effect 1.
Enjoy your ME2, as is.