Enhancing near-ascended powers
Amara, an Ancient who was left on Earth when Atlantis left for the Pegasus galaxy, was known to have possessed one of these devices, and was wearing it when she was placed in a stasis pod on the Greek island of Santorini, the original construction site of the City-ship of Atlantis.
When she was freed from this pod roughly ten thousand years after entering it, she used the amplifier bracelet to create an energy blast which took out the three Tau'ri members of the Trust who had opened her pod. Cassandra Fraiser, who had been captured by the group, was able to defend herself from the blast using her own powers.
Amara would later use the amplifier bracelet to create a wormhole from Stargate Command to Atlantis in order for her to go to the city to cure the Ancient contagion which was running amok. Shortly before her death, Amara handed the bracelet to John Sheppard with instructions to hand it to Cassandra. (SG1: "Transitions")