The Time Bracelet is an ancient relic handed down by the Guardians of Time, a sect group of guardians that involve the stability and watch over the very fabric of time itself and is often related to both Celebi and Dialga.
The bracelet has the power to allow the wearer to travel through time, using the power that was blessed by Celebi. However it will wane in power over time and would need to be recharged by a Celebi. The power to time travel will work, but how far into the future or past one can go is reduced depending on the potentacy of the power that remains.
The only known Time Bracelet that exists in modern times is owned by Logan, and was a gift from Celei, and was infused with her time traveling ability shortly before the Primal Dialga incident on Spear Pillar and Celei's disappearance into the Rift. It was the only thing Logan had that reminded of his and her bond and wore it constantly, allowing for him to continue his journey, and be able to travel through time himself.
Now, the power has since wanned since Celei's return, as the bracelet can only take Logan ten years into the future or past, and would need Celei if he wanted to go further, as she feels there is no point in restoring the time traveling power in the bracelet. Now, he uses it as a his Keystone and a holder for his personal Latiosite for when he is in Eon form.
Most people he met never knew he had the bracelet as it is always hidden under his right sleeve, and only when he Mega Evolves any of his Pokémon.
Unlike the Soul Dew, the bracelet would disappear when Logan becomes a Latios, likely as it would easily come off his right claw, but can still tap into the Latiosite's power to Mega Evolve himself however.
The top image shows the front of the Bracelet, should an orante design around it, with a ruby and sapphire on each side of the braclet and the motif of the Time Guardians, which is made of a jade emerald.
The bottom image shows the rear of the Bracelet, which has a slot in which Logan has his Latiosite resting in.