Short answer: it was stolen in 1911, and the heist was very publicized, including numerous books on it. So began the era of Mona Lisa popularity, and since majority of people loves to like what majority likes, it's widely considered the best painting ever, among snobs and laymen. That's all there is to it, the painting nowdays is famous because it is famous.

Prior to the heist, some people considered it the best of Davinci, but they were in the minority. At best it was something vaguely similar to what we call a "cult classic" nowdays, a good work that has a small group of people idolizing it but has no real popularity and majority of people and critics do not consider it such a masterpiece. Mona Lisa used to be seen as just another good painting by Davinci.

There was a very good thread about this a year ago which you might find interesting.