From Wikipedia :

"[Rabindranath] Tagore wrote novels, short stories, songs, dance-dramas, and essays on political and personal topics.Gitanjali (Song Offerings), Gora (Fair-Faced), and Ghare-Baire (The Home and the World) are among his best-known works. His verse, short stories, and novels, which often exhibited rhythmic lyricism, colloquial language, meditative naturalism, and philosophical contemplation, received worldwide acclaim. Tagore was also a cultural reformer and polymath who modernised Bengali art by rejecting strictures binding it to classical Indian forms. Two songs from his rabindrasangeet canon are now the national anthems of Bangladesh and India: the Amar Shonar Bangla and the Jana Gana Mana." 

Being the first Indian Nobel Prize winner, it is only natural for Rabindranath Tagore to be so revered by the Bengali people.  However, the real love for Tagore comes from his literary work.  His work manages to touch the lives of every Bengali because the subjects are always of a simple nature.  Tagore used the life around him as inspiration for his work, which allows Bengalis to connect to his life's work at a very fundamental level.