A "buckle" is the part of a belt where you attach the two ends to each other. The belts people wear on their pants have buckles. So do some shoes, straps for handbags and luggage, and seatbelts.
When an adult wears a seatbelt, you say that they're "buckled up". But when you put a child in a car seat, you buckle them in. The difference is that a person who's "buckled in" has straps not only across the waist, but over both shoulders as well. Jet plane pilots also get "buckled in".