The rules are complicated as to when women should wear head coverings and when it's not necessary.
The general idea is that in the organization, men are given the responsibility of leadership. Women play a supporting role and are to be in submission to men.
In certain situations, women wear head coverings out of respect for baptized males. A head covering is not required all the time.
Instead of going into countless senarios, here is a simplified explanation of what Jehovah's Witnesses believe. It is a quote from one of the organization's publications. It summarizes the reason why women wear head coverings and when it is necessary.
'Praying or preaching in the Christian congregation is normally the responsibility of a man. Hence, when a Christian woman cares for matters pertaining to worship that ordinarily would be performed by her husband or by a baptized man, she should wear a head covering.' Watchtower Magazine, July 15, 2002, Questions from Readers, 'In what situations is it appropriate for a Christian woman to wear a head covering for spiritual reasons?'