Roddy Doyle writes The Commitments from the third person point of view, using he, she, and it, but with limited omniscience. This means Doyle sticks closely to one character. In this case, he filters the story through the character of Jimmy Rabbitte and his experiences managing his musical group The Commitments. It is Jimmy who advertises for band members, gets them together, and finds them gigs.
The third person perspective works well for this story. It allows the reader to get close to all the characters and get an overall sense of what's it's like to be in a band. The author could have quite easily written it in the first person, using Jimmy as a narrator, but that would have sidelined the other characters and made it feel like it was all about Jimmy's journey. In addition, Jimmy is only the manager. The use of the third person marks the band out, and no particular person, as the most important element of the novel.
The story describes the band's rise and fall. As soon as they start making progress, the band members begin to disagree with each other and eventually split up. The book ends with Jimmy, Outspan, Derek, and Mickah talking about starting another group.