The peculiar experience of seeing/hearing/reading/experiencing something for the first time, and being relatively unimpressed by said thing. Then, when said thing is revisited on multiple successive occasions, it increasingly grows in one's estimation.

There are those who claim that the true Big Lebowski Phenomenon can only be attained when said thing is ultimately counted among the stratosphere of one's favorite things. Although the occurances of such a Utopian Big Lebowski Moment are admittedly few and far between, the satisfaction is said to be exponentially greater.

The Big Lebowski Phenomenon derives its name from the eponymous Coen Brothers film. Many exited the theatre, having seen it for the first time, feeling distinctly underwhelmed; the critical response tended to match this feeling. However, on repeated viewings, especially on video, these same masses have noted that it mysteriously seems to get better and better. The experience became widespread enough that the film's title was forever attached to the phenonmenon.

Not that while the BLP is often used in reference to cinema, its applicable uses extend far beyond film stock. Also note that the BLP is a peculiarly individual occurence.

A few noted examples:
The movie Out of Sight
The Kevin Smith movies Mallrats and Dogma
The beverage beer (esp. the sub-catagory of Guinness)