What's the meaning of the "kid" claim in a JWT token?

kid is an optional header claim which holds a key identifier, particularly useful when you have multiple keys to sign the tokens and you need to look up the right one to verify the signature.

Once a signed JWT is a JWS, consider the definition from the RFC 7515:

4.1.4. "kid" (Key ID) Header Parameter

The kid (key ID) Header Parameter is a hint indicating which key was used to secure the JWS. This parameter allows originators to explicitly signal a change of key to recipients. The structure of the kid value is unspecified. Its value MUST be a case-sensitive string. Use of this Header Parameter is OPTIONAL.

When used with a JWK, the kid value is used to match a JWK kid parameter value.

The kid (key ID) claim is an optional header claim, used to specify the key for validating the signature.

It is described here: http://self-issued.info/docs/draft-jones-json-web-token-01.html#ReservedHeaderParameterName