Much like HTTPS, the trust in C2PA is built on top of public-key cryptography. There are two main ingredients: the digital signature and the public key infrastructure (PKI).
The digital signature uses a public-private key pair. A message is signed by the private key, creating a signature of a fixed length. Then, the signature can be verified against the message using the public key. The verification guarantees (because math) that the message came from someone with the private key without revealing any information about the private key, so as long as the private key is kept secret, we know the message came from that someone.
The PKI then answers: who is that someone? After all, we can only trust the message as much as we trust that someone. This is where certificates come in. Each certificate contains a chain of digital signatures, each of which says "this is the identity of the below public key," with a trusted "root" identity securing the end of the chain. Furthermore, the PKI also maintains a list of private keys that have been lost, stolen, or otherwise compromised.
Lastly, oftentimes the message itself is not signed directly, but a cryptographic hash of the message is signed instead. This is because signing long messages is computationally expensive. This works because the cryptographic hash again guarantees (because math) the content of the original message.