They were all members of a family of Persian nobility who converted to Christianity and distributed their fortune among the poor, as was custom for Christians at the time. As a family -- Maris the father, Martha the mother, and the two sons Abachum and Audifax -- they traveled to Rome to visit the tombs of the apostles. The year was 270.
Unfortunately for our poor family, Roman Emperor Aurelian had just gotten finished with a mass purging of Christians (he had them all crowded into an amphitheater, shot with arrows, then had their bodies burnt). The family decided that it would be nice to gather and bury the remains of the martyrs, for which they were arrested, and subsequently tortured under the governor Marcianus.
The trip ended when Maris and his two sons were beheaded and Martha drowned in a well at a place that is now called Santa Ninfa, Italy (then Nymphoe Catabassi). The remains were buried in a catacomb by a woman named Felicitas. In 1590 their relics surfaced at Rome, where they now reside, partly in the church of Saint Adrian, partly in the church of Saint Charles, partly in the church of Saint John of Calybite. Before this time, though, they were pretty well known as martyrs and early saints -- they were mentioned in writings of Saint Gregory, and apparently at one time some of the relics were in the hands of Eginhart, son-in-law and secretary of Charlemagne, who put them in the abbey of Selghenstadt.
The feast day of all four is celebrated on February 19.