In Volume One of The Sandman (Preludes and Nocturnes), Dream is held captive for 70 years. After escaping and taking vengeance on his (only surviving) captor, he returns home, to the Dreamworld. Finding it in disarray, he realizes that he needs to recover his "tools," his totems of power, so that he can make things right again. He mentions that he has "placed too much of [himself] in the tools," implying that his tools (ruby, pouch of sand, and and helm) contain parts of his power and, perhaps, his being.
The Sandman #2 "Imperfect Hosts" page 16
He decides to quest for his lost tools, spending most of the volume in that pursuit.
After recovering his pouch and helm, Dream attempts to recover his ruby from a Justice League storage house (#5 "Passengers"). However, he is knocked out when he touches it, because John Dee modified it during his years of using it. While Dream is out, Dee takes the ruby, and wreaks global havoc with it for one day (#6 "24 Hours").
When that day is over, Dream asks Dee to return the ruby to him so he can attempt to fix all the things that Dee has broken. Dee, however, refuses, and threatens to kill Dream with the ruby.
The Sandman #7 "Sound and Fury" page 5
During that conversation, Dream says a little more about his relationship with the gem:
The Sandman #7 "Sound and Fury" page 4
Dream takes the battle to the Dreaming, where Dee appears to destroy Dream with the ruby; actually, he destroyed the ruby and transferred the power inside it back to Dream.
The Sandman #7 "Sound and Fury" page 20
What does the ruby represent? There's a lot going on around this ruby: it is an object that was created by an anthropomorphic personification of dreams, invested with his power and part of his being, that was stolen from him, rendered unusable to him, used to wreak global chaos, destroyed in an attempt to kill its creator, and ultimately returned its power to Dream.
I am not very well-versed in mythology, but I am fascinated by the ruby and Dream's relationship with it. I would appreciate answers that involve mythology (as Dream has connections to mythology), but answers with other sources are also acceptable. Like I said, there's a lot going on with this gem, but answers don't need to explain all of it (good answers, like scientific theories, will explain as many facts as possible; the more things explained the better).