Typically in Christian theology, but in many other religions' theologies too, a dogma is an absolute theological foundation, that must be strictly held as an indisputable principle in order to be a faithful follower of that religion.
Dogma eminently distinguishes itself from theological opinions, or beliefs, about which the faithful are free to disagree, for its absolute character; as a fundamental part of the religion, it cannot be disputed, revised or otherwise doubted, but has to be respected by faith. However, dogmas can be discussed and even expanded upon, provided that doing so doesn't overturn or contradict the original teaching. The disagreement on dogmas is heresy and usually leads to the expulsion of the heretics from the religious group.
The specific beliefs on dogmas and their sources, can considerably vary among religious groups. For most of Eastern Christianity, the dogmas are contained in the Nicene Creed and the first two, three, or seven ecumenical councils (depending on whether one is a Nestorian, a Monophysite, or an Eastern Orthodox Christian). Protestants may also affirm these, but often rely on a "Statement of Faith" which summarizes their dogmas, drawn up by their individual denomination.
The term dogma has been imported in politics too, where it stands for a concept that expresses a substantial element of the ideological referring doctrine. Often, but not exclusively, said of the established party line of a political party, in the journalistic jargon.
It is commonly used, in everyday speech (even about politics), to indicate a fact that is considered absolutely self-evident by its believers, without thought to its accuracy or relevance or to different opinions on the same subject, particularly where the "dogma" is long established within a group or organisation.
Dogma is also the name of a thrash metal band. Their site is here.
Dogma is also the name of a movie comedy, directed and with screenplay by Kevin Smith, starring amongst others George Carlin as a Cardinal, Alanis Morissette as God, and Ben Affleck and Matt Damon as a duo of fallen angels. It caused much controversy in many countries, as well as resulting in a death threat for Smith.
Dogma 95 is the name for the manifesto about filmmaking aesthetics, made initially in Copenhagen in 1995 by four directors: Lars von Trier, Thomas Vinterberg, Kristian Levring, and Soren Kragh-Jacobsen.