A Cyc Server is a Cyc executable image running on some machine. In principle, more than one Cyc Server could be running on a machine, but the software currently assumes that there is only one per machine.
At a site using Cyc, the Cyc Servers share changes to their KB's by recording the operations in common transcript files. Cyc Servers which start with the same KB and which process the same set of operations ought to end with identical KBs.
This "loosely-coupled" multiple-server scheme allows many users to edit a shared knowledge base while retaining the advantages of using local copies of the data, such as good response time. It also provides the flexibility to perform local experiments without affecting other users. It's possible for two users to share operations which become contradictory when merged in the common transcript, but this happens infrequently and is not typically a problem in daily usage.
More than one user can be logged in to a Cyc Server via the Cyc Web Interface. In that case, the users need to cooperate carefully since they are all working in the same image and each can change system parameters that will affect the others. At Cycorp, there is typically one primary user for each Cyc Server, and that person is the one who may edit its KB. Others may log in and browse that copy of the KB, but they should only edit or modify system parameters with the permission of the primary user.
Usually, one Cyc Server is chosen to maintain the "reference" copy of the KB and at intervals its entire KB is written out to files. From the KB files, new executable images can be generated, incorporating all the changes from the old shared transcript.