Basic meaning and etymology
As a proper noun, The Kirk is an informal name for the Church of Scotland, the country's national church. The Kirk of Scotland was in official use as the name of the Church of Scotland until the 17th century, and still today the term is frequently used in the press and everyday speech, though seldom in the Church's own literature. However, Kirk Session is still the standard term in church law for the court of elders in the local parish, both in the Church of Scotland and in any of the other Scottish Presbyterian denominations.

The Church of Scotland
Even more commonly, The Free Kirk is heard as an informal name for the Free Church of Scotland, an evangelical presbyterian church formed in 1843 when its founders withdrew from the Church of Scotland. See:

Free Church of Scotland (1843-1900)
Free Church of Scotland (post 1900) High Kirk
Like words meaning "church" in other languages, kirk is found as an element in many place names in Scotland and northern England, and in countries with large Scottish expatriate communities. Examples include Falkirk or Kirkwall in Scotland, Kirkstall in England and Newkirk, Oklahoma in the United States. For a fuller list, see Kirk as a placename element.
What may be slightly surprising is that this element is found not only in place names of Anglo-Saxon origin, but also in some Southern Scottish names of Gaelic origin such as Kirkcudbright (where the second element is the Gaelic form of "Cuthbert"). Here, the Gaelic element cil- (church, monk's cell) might be expected. The reason appears to be that kirk was borrowed into Galwegian Gaelic, though it was never part of standard Scottish Gaelic.
When the element appears in placenames in the former British empire, a distinction can be made between those where the element is productive (the place is named because of the presence of a church) and those where it is merely transferred (the place is named after a place in Scotland). Kirkland, Washington is an exception, being named after a person.
The element kirk is also used in anglicisations of continental European place names originally formed from one of the continental Germanic cognates. Thus Dunkirk (France) is a rendering of an original Dutch form, Duinkerke.
See: David Dorward, Scotland's Place-names, 1995, p.82f. ISBN 1-873644-50-7