What it means
Chops is a jokey, a bit old-school way to mean your mouth, lips, or jaws. You hear it in stuff like shut your chops when someone's yapping too much. In lick your chops, it means you're getting properly excited, usually about food. Bust someone's chops is mostly US and means to hassle them, nag them, or give them a hard time.
Usage examples
"Soon as the chippy opened, Gaz was licking his chops like a seagull at Brighton. I’m like, stop busting my chops, I’m ordering two portions, alright?"
"Kid had jam right round his chops by ten in the morning, the high chair looked like a Jackson Pollock and his nan was already laughing too hard to clean it."
"My uncle was licking his chops the second he saw the rib of beef come out of the oven, he had been planning Sunday lunch since Wednesday night, gravy already poured."
"Oi, shut your chops for two seconds and let me hear the postcode they're calling out."
"He was licking his chops when the wings landed, acting like he'd not eaten since Christmas."
Where it comes from
Chops for the mouth or jaws goes back to older English use of chop meaning jaw or cheek, recorded from the 16th century and linked to biting and animal jaws. The sense stuck around in comic everyday speech, then American English built extra phrases on top of it, like bust your chops.