The dance sequences in Hindi (and other Indian language) films are definitely examples of escapism, but I think the reason for their popularity is quite complicated...
Once upon a time Indian cinema actually produced serious, substantial (and very good I might add) movies such as Charulata and Devi (directed by Satyajit Ray) but it seems to me that around the same time as Satyajit Ray's most famous movies (1960's) musical films began to surpass conventional dramas in popularity. The movie that stands out in my mind as pretty much the mother of all modern Bollywood films is Mughal-e-Azam by K Asif. While not the first musical Indian film, I think it solidified the place of musical films in Indian culture.
But why the popularity?
DancerJack is absolutely correct about dance playing an integral part in Indian religious and historical narratives. No matter where you are in India there is some local form of dance that has been used for thousands of years to tell stories from the Ramayan, the Bhagavad Gita and other texts as well as historical tales of battles etc. In the Mughal (Muslim rulers) courts of North India, Kathak also developed as a dance of courtesans but it too was used to tell stories - just usually tales of love or something like that. SO, dance is definitely important to India historically. But I think there's more... Here is my theory:
Right around the 1960's technicolor was just hitting Indian cinema. As a result dance sequences could look truly magical, especially to the average Indian who would be lucky to ever see such grandiose performances live (Watch Mughal-e-Azam if you want to see the first BIG technicolor dance sequences. Even by today's standards they're pretty impressive). Simultaneously, India and Pakistan were in the throes of a violent partition that was sending ripples throughout the subcontinent. As a result many Indians wanted some sort of escapist relief and they turned to movies. Movie makers took advantage of this by crafting stories around values that Indians hold very dearly (such as self-sacrifice for one's family) and a newer fantasy: the reunion of India and Pakistan. Additionally, many movies focus on love stories - something that would rarely, if ever, actually happen in a culture where arranged marriage is the norm. This is why so many Hindi movies center around familial or romantic conflicts in which the characters are divided but ultimately come back together again in the end. Plus, who doesn't like a good melodramatic plot every now and then?