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1.
This phrase means exactly the same as a fly on the wall -- that is, somebody who covertly watches or listens in on something that is not intended for them to see or hear.
From the Star Trek: The Next Generation episode, "Lower Decks":

"How would you like to be a spider under that table?"
"What?"
"A spider under the table."
"Is that like a fly on the wall?"
"I guess so."
by Telephony August 29, 2014