Seth Meyers is seen nightly hosting NBC’s “Late Night” and heard weekly through his two podcasts, but as the comedian and writer is quick to point out, the bulk of his time is spent being a father and a husband. Which is why, for his second-ever stand-up special “Dad Man Walking,” he largely ditched the sharp political material that is a staple of “Late Night” in favor of material about his wife and three kids.

“That’s where all my material comes from,” Meyers told TheWrap of his special, which premieres Saturday on HBO (his first for the network). “I think there’s that thing, before you have a wife and children, you’re like, ‘I don’t know why people write jokes about that,’ and then you have it, and you’re like, ‘Oh, because it’s the entirety of your existence.’”

The special finds Meyers lovingly but cuttingly discussing his home life,...