NIMBY is short for "Not In My Back Yard." I.e. it is rejecting something being built nearby. It is a negative term implying that the reasons for the opposition are selfish and not in the community interest.
It often relates to a form of development which needs to be built somewhere, but is perceived to affect property values or make life difficult in some way. Examples of such development could be medium and high density housing development, or a halfway house for mental ill people, or treatment center for drug addicts.