The aesthetic appreciation of Da Vinci's work would make it a cultural icon.  The portrait is a study in painting technique with its technique in both subject display, texture, foreground, and background, as well as symmetrical designs.  It is something that has come to be appreciated as a landmark art work.  I think that its vaulted viewing position at the Louvre has also helped to contribute to its cultural icon status.  People go to the Louvre, in large part, to see the Mona Lisa.   This is only enhanced by its staging in bulletproof glass, impermeable to the elements that could wither paintings like it, and to ensure that individuals who view it recognize that they are standing in the presence of something iconic.  At the same time, the wealth that the painting could generate on the open market continues to add to its iconic status.  I also think that the fact that so many artists have referenced or parodied it do help to feed the idea of a status that represents iconic.  Warhol's pop culture interpretation of Da Vinci's work is only an example of this.  I think that one can get the full effect of Da Vinci's work's iconic stature by surveying the internet to see what a search of the work results.  The images seen are both representative of the legacy of the painting and how it has become iconic in so many different ways.

Why is The Mona Lisa by Leonardo da Vinci so famous?

While many viewers of Mona Lisa, or La Jaconde, as the painting is called in the Louvre in Paris where it hangs, are initially diappointed in the smallness of this portraiture, they are intrigued by the enigmatic quality of the subject's expression and the subtlety of forms and atmosphere of this portraiture. 

Indeed, the Mona Lisa has long been the object of many analyses and discussions from the debate on the actual subject of the portraiture (many believe it is Lisa Gherardini, wife of an influential merchant of Florence, Francesco del Giocondo), the mathematical examination of the equilibrium of the painting, to the unique suggestion of sculpture in the lady's predominance over the rest of the painting, to the "melting" of the contour of the figure so that it is led around it in imagination.  This illusion of movement has been called by critics "the breath of life" in the portrait.

These qualities of movement and ambiguity of character--the famous unsymmetrical smile, for instance--are innovative techniques for daVinci's time.  Another striking technique of da Vinci's is his creation of mood with the soft play of shadow and light over the features, the hazy blending of the figure with the landscape that gives an organic unity of living things with rock and water.

When the portrait was first displayed, it was the technical mastery that initially awed observers,

the delicacy of the chiaroscuro, the exquisite modelling of the lips, eyes, hands, the compositional harmony of it all,

but now, perhaps, it is the mysterious power of the portrait which makes it most renowned. For, the Mona Lisa is not explicable by formal means alone and opinions are greatly varied. Walter Pater's celebrated efforts are noted,

She is older than the rocks among which she sits; like the vampyre she has been dead many times, and learned the secrets of the grave...

Further, Pater compares her to Leda, the mother of Helen of Troy, St. Anne, the mother of Mary.  But, in sharp contrast to his efforts to define Mona Lisa, the skeptical Duchamp critiqued her by defacing the portrait with a moustache on a postcard, subsribed by an obscene description. And yet, both acknowlege Mona Lisa as a lay icon, an image that remains all things to all men. And, this, perhaps, is why Leonardo da Vinci's Mona Lisa is so very famous.