Kildigs acts as Shukhov's counterpart for the bulk of the novel. Kildigs is a fellow bricklayer and a fellow skilled laborer, and he works alongside Shukhov throughout the work day. The two men are similar in many ways, but Kildigs has a few traits that definitely set him apart from Shukhov.
First off, Kildigs is a comedian. He's always joking around apparently. More on the "apparently" shortly. Here's what Shukhov has to say about him:
He'd been in the camp only two years, but he knew what was what: you get nothing by asking. [....]
Every word from Kildigs was a joke. The whole gang loved him for it. And the Latvians all over the camp had tremendous respect for him. But then, of course, Kildigs could count on a square meal, he got two parcels every month. [...] He could afford to see the funny side. (289-293)
This is pretty much Kildigs in a nutshell here. He's Latvian, he's very smart and knows how to take the initiative (like when he suggests they steal tarred paper for the Power Station), he's respected, and he tells lots of jokes. The last one is something we have to take Shukhov's word for though. Working at a breakneck pace all day isn't really conducive to jokes and conversation, so we don't actually get to hear much of Kildig's famous humor.
Regardless, it's probably more important that we know Kildigs has a sense of humor as opposed to seeing it in action all the time. Kildigs gets packages, and that detail is key to understanding his character, and the vital role packages (which signal outside world help and support) play for prisoners. As Shukhov notes, people who get packages are healthier and stronger and can afford to joke around sometimes. Shukhov, who never gets any mail, is too busy trying to score some extra food to think up jokes.