Biblically, dogma refers to a decision or teaching that is considered authoritative. In Acts 16:4, during Apostle Paul's second missionary journey, he and his fellow travelers delivered to believers the decisions (decrees) arrived at by church leaders regarding (primarily) the role of circumcision in salvation (see Acts 15).
And as they (Paul, Silas and Timothy) passed through the cities, they delivered to them (the churches in Galatia, Macedonia and Achaia) the decrees (Greek: dogma) to keep, the ones that had been decided upon by the apostles and the elders in Jerusalem (Acts 16:4, HBFV)
Concerning the modern religious meaning of the term, the Pocket Dictionary of Theological Terms states "In Protestant circles dogma is nearly synonymous to doctrine, that is, a theological teaching. In Roman Catholic and Eastern Orthodox circles (they) are the officially accepted teaching of the church . . . "
A related term, dogmatics, refers to the systematizing and summarizing, by a religious group, of their understanding of the Bible into theological categories such as Christology, prophecy and so on (ibid.). In many churches, the rejection of teachings strongly supported by church leadership is considered heretical and may lead to a person being expelled (excommunicated, disfellowshipped) from the religious group.
Roman Catholics do not consider all their religious teachings as dogma but only those that are officially deemed as such. These include the belief in a Triune Godhead, the immortality of the soul, Papal infallibility and the Immaculate Conception of Mary.
The most recent Catholic teaching declared dogmatic occurred in 1950, when Pope Pius XII elevated the doctrine of the Assumption of Mary (the belief that the body of Jesus' mother, upon death, was literally taken to heaven) to this level.
As the Bible is multiple-redundant, no verse or group of verses should be used as a basis for dogma or religious tenant unless it agrees with the rest of Scripture.