|Photo by Fir0002/flagstaffotos (GFDL license)|
I introduced molecules, and proteins back in this post. Proteins are the key molecules used to make organisms, an organism's DNA are the instructions to make a set of proteins. Spider silk is made from protein. A spider is able to produce a whole range of silks with different physical properties: dragline silk is used to make the outer-rim and spokes of a web and is strong and tough; capture-spiral silk is sticky, stretchy and tough; tubiliform silk is used for egg cases and is the stiffest; aciniform silk used for wrapping prey is the toughest; minor-ampullate silk used to make temporary scaffolding for building a web (it's not as strong but very stretchy). From a technical point of view "strong" refers to how hard it is to stretch something, and "tough" refers to how hard it is to break something. Spider silk is similar to silkworm silk but it is stronger and more extensible.
Not only is spider silk interesting of itself, but from a material scientist point of view, it really isn't fun to make and use new polymers (you need to build expensive plant to make them, you need to work out your ingredient supply chain, you need to check for safety and environmental problems). If, on the other hand, you can get the properties you want from one of your pre-existing polymers by changing the microstructure then life is much easier. Spider silk may provide hints as to how this might be done.
Update: Curtesy of @happymouffetard, the evolutionary origin of spider-silk spinnarets appears to be hair follicles, according to this article.
*Thanks to Stephen Curry for pointing me to the "spiders on drugs" video.