The noun impairment means that some ability is not as strong as normal. People can be:
hearing impaired
visually impaired
mentally impaired
An impairment can also be temporary - your judgment and coordination become impaired when you drink too much alcohol, for example.
Both disability and handicap refer to a problem that prevents someone from doing normal or typical activities. People who have such problems are sometimes described as disabled or handicapped people, although the best term is to say someone has a disability or, when talking about these people as a group, to say people with disabilities.
When a building or other structure has special accommodations for people who use wheelchairs or who have other mobility difficulties, we often call these handicap-accessible places.