A hardware security module (HSM) is a physical computing device that safeguards and manages digital keys for strong authentication and provides cryptoprocessing.
In DDoS mitigation cloud services, HSM is used to securely upload a sensitive certificate to the provider. The provider requires your certificate so it can scrutinize it for DDoS attacks inside the encrypted traffic.
Some providers do not have HSM as part of their service, and therefore there is some risk in providing them with a most sensitive asset such as the certificate. The HSM reduces this risk.