Though Paul calls this disciple Cephas, he's probably better known as Peter (John 1:42). As in Simon Peter. Jesus' right-hand man. Yeah, that guy.
Paul mentions him briefly in the same breath as Apollos. Apparently, some of the people in Corinth have decided to follow his teachings instead of Paul's or Apollos' (1 Corinthians 1:12). Hey, it's always good to have options.
But, Cephas/Peter also doesn't seem to be in the same class as Apollos. First, it's not clear that he's even spent much time in Corinth. It's possible that his teachings have gotten some leverage because he's such a well-known apostle. And because Peter and Paul didn't always see eye-to-eye, it could be that those who claim allegiance to Cephas are actually just interested in a more Jewish way of worshiping Christ. Maybe they think all Christians should be circumcised or keep kosher. Paul would be checking the "no thank you" box on both of those.
Paul also mentions that, unlike him, Cephas/Peter has a "believing wife" (1 Corinthians 9:5). This jives with the gospel account: Matthew 8 mentions that Peter has a mother-in-law. Paul drops this tidbit, too: after Jesus was crucified, "he was raised on the third day [and he] appeared to Cephas, then to the twelve" (1 Corinthians 15:4-5). This is a little off. All four gospels show Jesus appearing first to his female followers. Why no love for the ladies, Paul?