Web of Trust tries to solve the same problem as PKI in a decentralized way, i.e., without the Certificate Authorities (CA). To achieve that, it allows users to vouch for other users, e.g. John says that Mary is who she says she is, and that her public key is X. If several people, maybe known in real life, claim that a public key corresponds to Mary then others will be more inclined to trust it. Since there are several such trust connections between the participants, it is called a web of trust.