Betty is in a comatose state at the beginning of the play because she is traumatised by recent events. First, she has been taking part in dubious activities such as dancing (a strictly illicit practice in the Puritan community of Salem) and she has also witnessed Tituba's attempts at black magic (apparently at Abigail's behest). Also, she was discovered dancing along with the other girls, by the minister, Reverend Parris. All this has had a deeply upsetting effect on her and her reaction is, in effect, to go into shock.
We cannot be certain if Betty is really unconscious or pretending to be so, but in either case the reason is because she has been so frightened. People like the superstitious Mrs Putnam, and the foolish, easily influenced Reverend Parris, think that she has been bewitched, but more sensible members of the community, like the elderly, kindly Rebecca Nurse, are aware that there is a naturalistic explanation. Rebecca advises the others to 'pray calm yourselves' and goes on:
I have eleven children and I am twenty-six times a grandma, and I have seen them all through their silly seasons, and when it come on them they will run the Devil bowlegged keeping up with their mischief. I think she’ll wake when she tires of it. (Act I)
A mother and grandmother, Rebecca recognizes that Betty's own childish ways and emotions are responsible for her condition, rather than any more sinister reason. She has been terrified that she will get into trouble for her recent misdemeanours. It is significant that she revives only when Abigail shifts blame away from all the girls by accusing others of witchcraft.