The Spider refers to its web as a parlour from the very first line of the poem.

“Will you walk into my parlour?”

Actually, “Walk into my parlour” or “Step into my parlour” has often been used as an aphorism to indicate a false offer of help or friendship which is actually a trap. That is why the poet chooses to use the word ‘parlour’ in the Spider’s voice to indicate to his evil intentions with the Fly whom he was extending an invitation.