When you are given a public and private key, you often need to provide other people with your public key. If you sign a digital document (using your private key), the recipient of that document will need your public key in order to verify your digital signature.
The inherent problem with a key is that it does not provide any information about the identity to which it belongs; a key is really just a sequence of seemingly arbitrary numbers. If I want you to accept a document that I digitally signed, I could mail you my public key, but you normally have no assurance that the key (and the original email) came from me at all. I could, of course, digitally sign the email so that you knew that it came from me, but there’s a circular chain here -- without my public key, you cannot verify the digital signature. You would need my public key in order to authenticate the public key I’ve just sent you.
Certificates solve this problem by having a well-known entity (called a certificate authority, or CA) verify the public key that is being sent to you. A certificate can give you the assurance that the public key in the certificate does indeed belong to the entity that the certificate authority says it does. However, the certificate only validates the public key it contains: just because Fred sends you his public key in a valid certificate does not mean that Fred is to be trusted; it only means that the public key in question does in fact belong to Fred.
In practice, the key ...