The background to the signing is, on the one hand, the verifiability of the sender. On the other hand, it serves as tamper protection. This means that the recipient can understand whether the content of the e-mail reaches him unchanged.

How does signing work?
A checksum of the content is formed and overwritten with the sender’s private key. Checks can then only be carried out with the sender’s public key.

Basically, any e-mail program can do this, but a personal S/MIME certificate is required. A domain certificate is not sufficient.