Dad: Son, what is the difference between a Bitcoin address and a Bitcoin public key?

Son: Hi Dad,

That's a good question! An address represents a hash of a public key of an asymmetric key pair.

The owner of the key pair can use the private key to sign transactions or messages.

Dad: Why sign a message?

Son: For example, to prove ownership of an address.

Only by using the correct private key a valid signature may be created, which then anyone can verify as valid by using the associated address which, again, represents the public key.