Certificates are the way that the signer can vouch for the signee. If you trust the signer, then you can trust the certificate and the signed public key. If you trust the signee, you can ignore the certificate.
In more real world terms:
Example 1: Cindy Certificateauthority is very well known. Everyone knows Cindy. Cindy has a really good reputation for verifying who people really are before she introduces them to other people. Someone claims to be Pablo Pubkey - a well known and trustworthy salesman - wants to sell you something. Cindy introduces you to this person and says that he's Pablo. You trust Cindy, so you believe that the person is Pablo, and so you decide to give Pablo your credit card number and buy stuff.
Example 2: You grew up with Freddy Friend since you were a child. You know who Freddy is - you met him in kindergarten and seen him become an adult alongside you. Freddy is also a salesman. If you want to talk to Freddy, you just go find Freddy - you don't need anyone to introduce you to him.
In the first example, you relied on a certificate authority whom you trust to tell you who owns a particular public key. In the second example, you had direct trust in the public key and didn't need a third party to tell you who owns it - for example, your software may issue public keys to its users and associate those public keys in your software's database. This second example is exactly the same when you have a self signed certificate and an unsigned certificate.