A client engine is a shared code base for a client with multiple sites hosted on ePublishing. These are referred to as Jade-CLIENT. Some examples are Jade-WATT, Jade-BNP, Jade-AHC.
What this means for you: This shared code base allows an update to be done to the client engine, and the update be pushed out to all of the client sites at once. This allows for strong consistency between sister sites, reduced development costs, and easier long-term maintenance.
On a weekly basis, the client engine is updated with the ePublishing master code base updates (Jade). The client engine, in turn, updates all of the client sites associated with that client engine to include all ePublishing master code base updates, all of the client engine updates, and any site-specific updates or bug fixes. This process updates all of the client's sites. Those updated sites are released to PRODUCTION (or live on your website) every Tuesday night.