By "primary system", I meant the initial system(s) interacted with in a distributed environment. Assuming a connection based distributed model (e.g. TCP/IP), there is a system on the other end of the connection to which a client is communicating. Even for connectionless models, in my mind the "primary system" would be defined as the set of systems which could possibly respond to a client's request.

Perhaps the term "primary" is not the best fit for this role. It just seemed less verbose than saying something like "the set of systems for which a client is directly aware and may interact with."