This track and I'm so tired are some of my favorites on The White Album.
From wikipedia:
The subject of the song is Prudence Farrow, a sister of actress Mia Farrow, who was present when the Beatles went to India to study with Maharishi Mahesh Yogi.
Farrow became so serious about her meditation that she "turned into a near recluse" and "rarely came out" of the cottage she was living in. John Lennon was asked to "contact her and make sure she came out more often to socialize". As a result, Lennon wrote the song "Dear Prudence". In the song Lennon asks Farrow to "open up your eyes" and "see the sunny skies" reminding her that she is "part of everything". The song was said to be "a simple plea to a friend to 'snap out of it'". Lennon said later that "She'd been locked in for three weeks and was trying to reach God quicker than anyone else."
I just can't imagine being named Prudence...
Prudence actually lives in the Panhandle
As I understand the story she was in India at the same time as the Beatles. She however preferred to stay indoors and meditate;
hence "Won't you come out and play ?"