its a service from Blockstream aimed at regulated assets on Liquid.

The usecase is something like: you want to issue a tokenized security on Liquid. Because of regulatory requirements, only registered investors are allowed to trade that token, but you want it to be freely transferrable between anyone who is "allowed".

So the way that it works is people use an AMP-enabled wallet. That wallet gives them a unique ID. The register that ID with whatever company who then puts them on a whitelist. When you receive an asset into you AMP-enabled wallet, it goes into a 2/2 multisig where you hold one key and the AMP server holds the other key. When you want to send the asset to someone else, your wallet signs and then the AMP server signs but ONLY if the destination address is on the whitelist.

The whitelist can be updated anytime without needing to re-roll all the UTXOs (which is something you'd have to do with a covenant), and is cheap and easy to manage.

It's literally a service to do whitelist-only token transfers for something that's bitcoin-compatible.

The "covenants will create whitelists/blacklists for bitcoin" thing is fud. it already exists.