How does the sting help Bilbo in his fight?

In Chapter Eight, Bilbo is alone in the dark and after trying to find his friends, he gives up and goes to sleep. He is arrested in his sleep, attacked by a giant spider that was trying to poison him. Bilbo kills it with his sword (Sting) and then he, himself, falls down and passes out. When he wakes up he finds his friends swaddled in spider net, suspended from tree branches and guarded by a troop of spiders. Bilbo's invisibility and sword help to get some of the dwarves free. Things improve when Gandalf returns to offer assistance, but in the end, Thorin is missing and he must be rescued from the king of the wood-elves.