Mr. Creakle is the headmaster of Salem House, David's first boarding school. He is acquainted with Mr. Murdstone. When David arrives for his first term, Mr. Creakle orders Mr. Mell to give David a sign to wear around his neck. The sign says, "Take care of him. He bites" (5.136). Mr. Creakle only takes the sign off David once he realizes that it gets in the way of the beatings Mr. Creakle frequently wants to give him. He is an abusive bully with no greater purpose in life than to punish boys; he has about as much interest in education and scholarship as a rock does.
Getting back to the "he bites!" sign, Mr. Creakle takes this warning from Mr. Murdstone – which is a reference to the bite David gives Mr. Murdstone when his stepfather is beating him – as a kind of challenge. As soon as he meets David, Mr. Creakle tells David that Mr. Creakle is "a determined character" (5.18) who likes to get his way.
Mr. Creakle also has a "tooth," a switch that he likes to use to beat the boys as often as possible. He clearly gets some kind of sadistic pleasure out of doing it. We find it truly icky that he particularly likes to whip the fatter boys because he likes the look of the cuts on their skin – Traddles is particularly plump, so he gets whipped every single day.
Basically, Mr. Creakle has no role in the novel except to be a tormenter of the young David. He does have one curious epilogue, though. Totally out of the blue, once David and Traddles have both risen to fame and fortune in their respective professions, they get invitations from Mr. Creakle to come and tour a prison in his district. Mr. Creakle has become a magistrate in Middlesex (a magistrate is a local judge, by the way).
David and Traddles can't help but notice that Mr. Creakle is kinder to his prisoners than he ever was to the boys at Salem House. David comments: "he is the tenderest of men to prisoners convicted of the whole calendar of felonies [...] though I can't find that his tenderness extends to any other class of created beings" (61.33).
They also can't help but notice that two of his prisoners are familiar: Uriah Heep and Littimer. Mr. Creakle is so stupid that he doesn't realize that these two are lying when they tell him they have reformed. He views them as model prisoners. This odd little episode in Chapter 61 allows Dickens to get in a dig at prison reform, which he felt should receive lower priority than making schools actually livable for children.