Its exuberance, violence, sadness, gentleness and romantic side, as well as the war-like tendencies of the White European-ethnic-American Jets and the newly-arrived Puerto Rican Sharks, who are battling for turf on New York City's West Side, and then end up battling over the love that Tony, the Jets founder and ex-leader, develops and nurtures for Maria, the younger sister of Bernardo, the Shark gang leader, combined with a strong cast, a strong story, and lots of style in terms of acting, the costumes and the fabulous cinematography by the late Daniel Fapp, are all combined into a genuinely dynamite-filled package that does rock.
Neither side approves of Tony and Maria's romance...that's for sure. Tony and Maria's love persists, however, despite Maria's initial reservations even though she loved Tony, Anita's clear disapproval of their romance, as well as the persistent tribal and ethnic loyalties, and friendships that existed within both of the gangs themselves, not to mention the continued hatred between the Jets and Sharks that resulted in the continued warfare between them.
Yet, at the same time, while West Side Story is proof that people from two very different racial/ethnic groups can and do fall in love, interstate and even marry, despite disapproval on the part of both sides, it's also proof that this same sort of disapproval can and does blow relationships apart, as well.
West Side Story, as a movie-musical rocks, however, not only due to the brilliant Bernstein musical score, the dancing, the cast and the very story behind it, but because it tells the story of the effort on the part of two human spirits to come together despite the constant conflict and warfare between the Jets and Sharks, and the possibility, despite the failure of that love to work out, due to the constant hatred, violence, and ultimately death.
As a movie-musical, West Side Story also has exceptional cinematography, the costumes are beautifully designed and appropriately colored, and the dancing is really superb. It showed Jerome Robbins at his best, and yet at his worst; the dancing was beautifully choreographed, and he understandably wanted perfection--to the point where people would drop, sometimes literally. (Eliot Feld, who played the part of Baby-John in the film version of West Side Story, actually collapsed from pneumonia during the filming of the "Cool" scene and had to be rushed to the hospital.)
Because everything about West Side Story is so integral and so vital to the story itself, this is a movie-musical that, if anything in it were to be omitted, whether it be by oversight or design, it could result in the decimation of this musical. If the romance scenes were taken out, for example, it would only be a story about urban gang warfare, which would leave it very one-or-two-dimensional, and rather myopic. If, on the other hand, the urban gang warfare between the Jets and the Sharks, the dancing, the Jet gang whistles, and the fingersnapping were left out, the same thing would happen, only to a more intense degree. The same thing would happen if the ray of hope in the form of a possible intergroup reconciliation in the end, after the deaths of Riff, Bernardo and Tony (two of whom were gang leaders and one an ex-gang leader), were to be taken out, as well, because a vital part of the message of West Side Story, as a whole, would be taken out. If the musical score weren't so intense and interesting, West Side Story, as a movie-musical, wouldn't be what it is, either.
All of the above having been said, West Side Story rocks precisely because there really is no other movie-musical like it; It is different from other musicals, in a very positive way. The double-edge message to West Side Story (i. e. the deleterious consequences of racial/ethnic/cultural hatred and prejudices, gangsterism and violence and death, and yet the ray of hope that shines through in the form of the hint of possible reconciliation between the Jets and Sharks.) is also what sets West Side Story apart from most other movie-musicals.
West Side Story, as a movie-musical, also rocks due to its rock-solid, but haunting beauty, that combines so much of everything, if one gets the drift. West Side Story also rocks, because it's so incredibly relevant, even today, with all the conflict that goes on, here in the United States and throughout the world. The fact that West Side Story is fiction that's also based on certain realities also makes this movie-musical rock.
All of that being said, West Side Story is popular because it rocks, due to its content, its relevance even to today's world, and because of its hard, eerie beauty.