The Collaborative International Dictionary of English v.0.48:

Spider web \Spi"der web"\, or Spider's web \Spi"der's web"\ .
   (Zool.)
   The silken web which is formed by most kinds of spiders,
   particularly the web spun to entrap their prey; -- also
   called cobweb. See Geometric spider, Triangle spider,
   under Geometric, and Triangle.
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The Collaborative International Dictionary of English v.0.48:

Cobweb \Cob"web`\, n. [Cob a spider + web.]
   1. The network spread by a spider to catch its prey.
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   2. A snare of insidious meshes designed to catch the ignorant
      and unwary.
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            I can not but lament thy splendid wit
            Entangled in the cobwebs of the schools. --Cowper.
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   3. That which is thin and unsubstantial, or flimsy and
      worthless; rubbish.
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            The dust and cobwebs of that uncivil age. --Sir P.
                                                  Sidney.
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   4. (Zool.) The European spotted flycatcher.
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   Cobweb lawn, a fine linen, mentioned in 1640 as being in
      pieces of fifteen yards. --Beck. Draper's Dict.
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            Such a proud piece of cobweb lawn.    --Beau. & Fl.

   Cobweb micrometer, a micrometer in which threads of cobweb
      are substituted for wires.
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WordNet (r) 3.0 (2006):

cobweb
    n 1: a fabric so delicate and transparent as to resemble a web
         of a spider
    2: filaments from a web that was spun by a spider [syn:
       cobweb, gossamer]
    3: a dense elaborate spider web that is more efficient than the
       orb web