multi-stage cryptographic computations One potential client is assessing our system by asking some questions to decide if they eventually will choose our service or not.

One of the question is 


  All multi-stage cryptographic computations are computed within the secure boundary of the HSM.


I Googled the phrase but I could not find any relevant topics to help me to understand the meaning of the question.

Could any of you give me some example of multi-stage cryptographic computations? Is it same as multi-party computation?
It might mean that any multi-stage cryptographic protocols – which require parties to store temporary data – could be weakened by exposure/tampering of this data. To ensure that does not happen, one needs to protect these intermediate chunks of data and (preferrably) the encryption process itself so that we can trust that, if the protocol finished successfully, it's results are to be trusted. 

One of the ways to protect it, is to offload all computations to HSM – which is compartmented from your regular process memory and thus is less likely to be tampered when your server gets compromised.