In Seventh-day Adventist beliefs, the "three angels' messages" is an interpretation of the messages given by three angels in Revelation 14:6-12. The church teaches that these messages are given to prepare the world for the second coming of Jesus Christ, and sees them as a central part of its own mission.
"The third angel followed them, saying with a loud voice, 'If any man worship the beast and his image, and receive his mark in his forehead, or in his hand, the same shall drink of the wrath of God, which is poured out without mixture into the cup of his indignation; and he shall be tormented with fire and brimstone in the presence of the holy angels, and in the presence of the Lamb: and the smoke of their torment will ascend for ever and ever: and they have no rest day nor night, who worship the beast and his image, and whosoever receives the mark of his name. Here is the patience of the saints: here are they that keep the commandments of God, and the faith of Jesus.'" (Revelation 14:9-12 KJV)
The third angel's message is a warning to the people of the earth, not to worship the beast or his image. (The "beast" and his "image" were introduced in chapter 13 of Revelation.) Those previous verses are the source of the famous mark of the beast.