The accommodationist approach to the separation of church and state opposes the separationist approach which has been dominant in the courts. According to accommodationists, the First Amendment should be read much more narrowly than it has been in recent years. Some go so far as to argue that the First Amendment prohibits the government from doing nothing other than creating a National Church everything else is permitted.
Such accommodationists will also tend to argue that, when it comes to religious matters (just as with other issues), majority rule should be the guiding principle. Thus, if the majority in a local community wants to have particular sectarian prayers in schools or during town council meetings, then that should be permitted.
Most accommodationists, however, do not go quite so far. As the name implies, the main principle upon which accommodationists base their position is the idea that the government should accommodate religious needs and the desires of religious institutions whenever possible. When it comes to the separation of church and state, there should not be quite so much separation and a bit more interaction.
Generally speaking, accommodationists favor:
Government funding for religious schools
Government organized and encouraged prayers (even sectarian) in public schools
Government funded religious displays (Ten Commandments, creches)
Government preference for particular religious holidays
Accomodationism was more common in the United States before the Civil War. During that time, there was much less separation of church and state because government at all levels took an active role in supporting, or at least endorsing, religion specifically, Protestant Christianity. Such support was assumed as a given and was rarely, if ever, questioned by religious minorities.
This began to change after the Civil War, when many groups tried to make the government endorsement of Protestant Christianity more explicit and extensive. This galvanized religious minorities, in particular Jews and Catholics, to become more assertive in their demand for religious equality.
Around the end of the 19th century, the public assumption of the validity of accomodationism began to erode as Jewish leaders advocated an end to Bible readings in public schools, the elimination of Sunday closing laws, and the repeal of laws designed to enforce Christian morality.