Mercury takes a UTXO as a building block and creates a system in which that one UTXO can be handed over to someone else.

This is facilitated by math! It comes down to this: s = s1 + o1 = s2 + o2.

Where s is the private key required to spend the UTXO. And s1 and s2 are the private keys of the facilitator (this is the guy you have to somewhat trust). And o1 is the private key of the original owner. o2, you guessed it, the private key of the new owner!

There are some provisions to make all of this safe and offline but in a tiny nutshell, this is it.

Caveat: I'm just learning about this as well