A meeting house is a building where religious and sometimes public meetings take place.

Meeting houses in America
The colonial meeting house in America was typically the first public building built as new villages sprang up. A meeting-house had a dual purpose as a place of worship and for public discourse, but sometimes only for “…the service of God.” As the towns grew and the separation of church and state in the United States matured the buildings which were used as the seat of local government were called a town-house or town-hall.

Many nonconformist Christian denominations distinguish between a

Church, which is a body of people who believe in Christ
Meeting house or chapel, which is a building where the church meets
The nonconformist meeting houses generally do not have steeples, with the term “steeplehouses” being used to describe traditional or establishment religious buildings. Christian denominations which use the term “meeting house” to refer to the building in which they hold their worship include:

Anabaptist congregations
Amish congregations
Mennonite congregations
Congregational churches with their congregation-based system of church governance. They also use the term “mouth-houses” to emphasize their use as a place for discourse and discussion.
Christadelphians
The Church of Jesus Christ of Latter-day Saints (Mormons) uses the term “meetinghouse” for the building where congregations meet for weekly worship services, recreational events, and social gatherings. A meetinghouse differs from an LDS temple, which is reserved for special forms of worship.
Provisional Movement
Religious Society of Friends (Quakers), see Friends meeting houses
Spiritual Christians from Russia
Some Unitarian congregations, although some prefer the term “chapel” or “church”.
The Unification Church

The meeting house in England
The Oxford English Dictionary states that a meeting house in England is always a “…nonconformist or dissenting place of worship…”

Source from Wikipedia