Why were the incidents with the spiders important in The Hobbit?

Thorin's company encounters the spiders in the deep forest
of Mirkwood in chapter eight, "Flies and Spiders" of The Hobbit.
This conflict is significant for two main reasons: 1) the spiders incapacitate the
dwarves, causing them to be easily captured by the elves, and 2) Bilbo's fight with the
spiders increases the hobbit's self-confidence in his own
abilities. 

The incident with the spiders had left the
dwarves tangled up in sticky webs and drowsy-minded from the spiders' poison; as Bilbo
rounds up and chases away the last of the spiders, the dwarves realize that Thorin is
missing.  The woodelves had "come to him, bound him, and carried him away" (151).  The
distraction of the spiders left the dwarves vulnerable to capture by the
elves.

Yet the ordeal with the spiders has a positive
outcome, for Bilbo realizes his own worth.  He defeats the great spider all by himself
"without the help of the wizard or the dwarves or of anyone else," which "made a huge
difference to Mr. Baggins" (142).  Bilbo gains confidence as a result and feels "much
fiercer and bolder" (142).