It stands for CLIENT_ID
.
From this MSDN blog post (emphasis mine):
Recently someone asked me what was the real meaning of the ‘Cid’ field which appears in the output of commands such as !process and !thread in the kernel debugger (kd). Though from a practical perspective I was aware that these represent the Process ID and Thread ID, I was unsure of what Cid stands for. In course of a search, I found a public source which answers the question. Cid is short for
CLIENT_ID
which in turn is an undocumented structure.
That posts cites that the original source as Undocumented Windows 2000 Secrets: A Programmer's Cookbook, by Sven B. Schreiber.