Colonel Pickering is the closest thing Pygmalion has to a father figure. He's a genial old chap, an expert in Sanskrit, and an all-around nice guy. He and Higgins hit it off right away, and without his suggestion, the whole bet would have never happened. Eliza credits Pickering's gentlemanly ways for starting her transformation from flower girl to duchess, for truly making her feel like a lady. He is the good cop to Higgins's bad cop (see "Character Roles" for more on this), the Sancho Panza to his Don Quixote. That said, he still gets carried away sometimes: he gets all worked up about "inventing new Elizas," he forgets to congratulate her on her achievement, and he ignores the many warnings that he and Higgins receive.
Pickering really is the epitome of the sidekick. He serves a counterpoint for Higgins, someone Higgins can bounce remarks off. His presence also allows for the humorous, effusive bit of Eliza worship at the end of Act 3 (3.226-244). Ultimately, Pickering adds a little more spirit and little more kindness into the mix.