(Click the character infographic to download.)
In a way, the Commander is the most naïve character in the book... which is super ironic given how much power he has. But, maybe you have to be naïve to succeed in Gilead (not to mention lucky enough to be a high-status man).
In his interactions with the narrator, the Commander comes across almost like an eager little boy, even though "he looks like a midwestern bank president" (15.2). The narrator guesses that he "want[s] [her] life to be bearable to [her]" (29.54), which is naïve—how could her life be anything but claustrophobic? Only someone who hasn't been deprived of his freedoms would imagine he could create a "bearable" state for someone who has.
The narrator interprets this as his rationalizing what's happened in Gilead: "If [her] life is bearable, maybe what they're doing is all right after all" (29.54). This gives the narrator, who basically has nothing, something to hold over the Commander—the idea that he wouldn't want her to die, and that he feels guilty about the Offred who came before her, who he had sex with secretly, too... and who killed herself.
As the narrator describes him, the Commander isn't all bad, as he loves reading and collects books. At first the kinky thing he wants to do—which the narrator is afraid of—turns out to be playing Scrabble and watching her read magazines. Yowza! Scandalous!
On the other hand, books aren't something to be doled out according to the kindness and whims of a kindly older gentleman; they're supposed to be for everyone. Ultimately the Commander's defining characteristic seems to be that he's lonely for intellectual feminine companionship. While sex ends up being part of the deal, it seems like what he's really looking for is a sympathetic ear. The narrator is disappointed to find out that the Commander thinks "his wife [doesn't] understand him. [...] It was too banal to be true" (25.64-65). In other words, the Commander's excuse for infidelity is a cliché. (Some things just don't change, even in a totalitarian dystopia.)
What really gets the Commander excited is having the narrator dress up in a naughty outfit and taking her to Jezebel's, where he can show her off in front of everyone. It's breaking the law, but not too much. As Moira says, men like him "get a kick out of it":
"It's like screwing on the altar or something: [Handmaids] are supposed to be such chaste vessels. They like to see you all painted up. Just another crummy power trip." (38.33)
Moira also says, of this Commander specifically, that "he's the pits" (38.31). Even, or especially, at Jezebel's, the narrator has sex with him because she has to, not because she wants to.
Professor Pieixoto has more luck determining the Commander's real identity than he does with any other character. If he is, as the professor suspects, someone named Frederick Waterford, he'll end up executed... in part for collecting reading material. If he isn't Waterford, what happens to him is anyone's guess.