Hamburger-kid is a cowboy character who's pretty much exactly what his name suggests—a guy with a hamburger for a head, decked out in full Western gear including the classic cowboy hat. He's got a lasso and rides around on a green horse called Pickles, which fans often note is a pretty memorable detail.
In Anpanman's world, Hamburger-kid serves as the protector of a Western-themed town. He debuted back on May 8, 1989, in the episode "Anpanman & Hamburger-kid," and the character stuck around—he's shown up plenty of times since then. There's even a dedicated DVD series featuring episodes centered on or heavily featuring him, so he clearly became popular enough to warrant that kind of treatment.
Content compiled by AnimeList.moe from publicly available sources.