What exactly do you mean by a socket? It looks to just be a filename on that summary. I assume this is not just redirecting stderr to your file of choice?
./cgminer -blah 2>/path/to/file
?
No it's not a file. It's a socket, just backed by a file instead of an IP address+port.
Something listens on the other end and does stuff with the data (like, forward to a master system).
Said other end can also send commands to you, since sockets are bidirectional; I haven't used BAMT yet, so no idea whether it actually does that or whether it uses the port just for reporting.