The noun “kid” in contemporary English is mostly used to informally refer to a child, e.g. “she’s just a kid” or “only 90s kids will remember”. However, the original meaning (which still exists but is rarely used outside the context of agriculture) is “a young goat”.
The meaning was extended to a “child” (from a “young goat”) in the late 16th century slang and became established in the mid 19th century. However, the origin of the word before that is even more interesting.
“Kid” is actually not a native English word. It is an early borrowing from Old Norse “kið” (“young goat”), and its descendants can still be found in modern Scandinavian languages, e.g. “killing” (literally “kid-ling”) in Swedish (also meaning “young goat”). However, the word “kid” itself in Swedish now means “a young deer”.
Finally, the English verb “kid” is probably derived from the noun via the meaning “to treat as a child”.