Trivikrama is one among the numerous names of Bhagavan Vishnu. The name Trivikrama comes from the giant form that he took during the Vamana Avatar. As he conquered the three worlds – sky, earth and underworld - with his feet – he got the name Trivikrama. The name and concept if more popular in South India.
Legend has it that the Asura, or demon, King Mahabali made the utopian kingdom a reality. His fame spread all over the earth and the netherworld and slowly into the heaven. Indra, the king of Devas and the ruler of heaven, felt threatened by the growing popularity of Mahabali. Aditi, the mother of Indra, observed a penance called 'payovrata' to help her son and pleased with her devotion Vishnu was born as Vamana, a dwarf, to Aditi.
Vamana approached Mahabali who was conducting a yajna. King Bali asked Vamana to choose anything that he wanted from his kingdom. Vamana asked for just three steps of land. And the king agreed readily.
Suddenly, the dwarf sized Vamana grew into the skies and with one step covered the earth and with another step the heavens. With no place to keep the third step, Mahabali offered his head, which was pushed by Vamana into the netherworld or pathalam. This unimaginably huge figure of Vishnu was called as Trivikrama by the people assemble there.
The story in detail can be found in the 8th canto of the Srimad Bhagavatam.