The double spiral is probably the oldest symbol known to man. It is carved into rocks from the earliest artworks, and is part of religious monuments.
It signifies the circle of death and rebirth, spiraling from one state to another. My little silver armband signifies to me the silver wheel, the wheel of stars where we dwell between lifetimes. I wear the band, and the silver spirals out of my arm and then back in, showing my spirit wheeling out of my flesh at the end of one life and returning at the beginning of the next.
But whatever else it signifies, it is still just a piece of cheap jewellry. This for me is particularly appropriate, since I believe strongly that it is this life we are in now that matters, and that we should live for, not the times between.