Another name for modalistic monarchianism, a Christian heresy popularized by Sabellius in Rome during the first quarter of the third century. "Sabellianism" is the name by which modalistic monarchianism was known in the Greek-speaking East; in the Latin West, the same heresy was more commonly called patripassionism.
Sabellius did not actually invent the philosophy that bears his name; that honour goes to Noetus, the bishop of Smyrna, who first proposed his flavour of monarchianism around the year 160. However, Sabellius' version of the heresy is the one that became most well-known, thanks to his highly publicized arguments with Hippolytus of Rome about Trinitarian theology, and his subsequent excommunication by Pope Callistus around the year 220.
Modalist monarchians wanted to preserve the oneness (monarchia, "single rulership") of God the Father at all costs. They feared that too much emphasis on the distinctness of God the Son had the danger of leading to a kind of polytheism. Thus they maintained that God was One, but that he had three "modes" in which he revealed himself to humanity. Just as the same substance can appear to us as water, ice, or steam, the monarchians explained, so also God can reveal himself in the world in three different ways. Another comparison might be to a man who is the father of one person, the husband of another, and the son of a third; he is a single being with three different functions or roles.
These ideas were expanded upon by one Marcellus of Ancyra, who died c. 374. Marcellus taught that the Monad revealed itself through time as Father, Son, and Holy Spirit. God the Father was understood as the Creator and the Lawgiver, and was associated with the "Old" Testament. As Son, which is to say in the revelation of the New Testament, the Monad revealed itself as the Redeemer. And finally, as Holy Spirit, living in the world now, it reveals itself as the giver of grace. All of these are aspects of the true God.
Though most Christians today recite the Nicene Creed and commit themselves in good faith to Nicene Christianity, many of them, deep in their heart of hearts, are modalists. When God "looks like" an old guy with a beard, telling people what to do, he is the Father. The God who "takes the form of" a young man who teaches lessons, works miracles, and eventually suffers and dies, is Jesus, the Son. And the Holy Spirit is simply God's breath or wind moving in the world. Since it is notoriously difficult to wrap one's head around the concept of the Trinity, modalism helps it all make sense. Technically, however, it is a heresy. The (small-o) orthodox position is that God is three distinct persons of one single substance.
Some contemporary Christian denominations are more explicitly monarchian. Oneness Pentecostals, also known by the pejorative name "Jesus Onlys", assert that the Father and the Son are one being without distinction.