Whilst it is obviously a marketing buzzword, encryption at rest (as opposed to encryption in transit (TLS)) is becoming more and more common.
This is mostly caused by the move the cloud (also known as someone else's computer). Admins at a cloud provider can essentially see all of your data. You would hope that most reputable providers would have appropriate access controls in place, but you are placing your trust (and possibly legal obligations) in them, not in your own employees.
By encrypting at rest with client keys you can protect your data from even the cloud operators, which has clear benefits for both parties.
The main reason encryption at rest has not been popular previously was that key storage is difficult. Within a company's network, if a database server is compromised, then it is highly likely that the key will be compromised too, so there is little point.