Outstanding - are you POTUS by any chance? I believe that George Bush asked the same question to Iraqi guests at the Whitehouse at the 2003 SuperBowl. Looks like, the answer wasn't made very clear for him.
Essentially, Sunni Muslims (globally the majority, by far - probably 90% of practising Muslims) accept only the authority of the Prophet himself - ie the final revelations of Allah as recorded in the Qu'ran. Shi'ites (an heretical sect to many Sunni Muslims) accept the authority of the 10 lineal descendants of the Prophet in addition to that of the Qu'ran. It is, of course, a bit more complex than this, but essentially this is the difference - at least, as far as I've been able to work it out from discussions with various imams!