It's called "metric reserve" for a very specific reason. "Metric" simply being a greek word rooted in "measure" and "reserve" because each "network"-which can be thought of as a currency-is made up of "reserve" accounts. Much like a traditional bank, someone is holding your physical money but you are allowed to spend it's value in the system. Unlike a traditional bank, metric reserve is a 100% reserve system. Users are not permitted to loan out or otherwise "tie up" reserve funds, as they must be ready at any time to transfer reserves to another connected account. Each user can have one reserve account per network. Each person ideally holds the same amount of reserves though they may all-and likely do-have separate balances.
Users only exchange reserves with other reserve accounts they are connected to. And users only are allowed to make payments with users who they are connected with-even if it's indirectly-on the same network. This network of connections is called a "graph" or "social graph" and corresponds to a Facebook-like "friend network". If there exists some path of connections between you and another user on the same network metric reserve considers those users to be on the same "tree". One of the two primary algorithms it runs is to determine which users are on the same tree.
Currently, in this implementation, metric reserve will prevent users who are not on the same tree from making payments even though they may both have positive balances on the same network.
The other primary algorithm metric reserve runs is related to answering the question, "How do we know how to spread out the reserves evenly when people are connecting and disconnecting randomly?" That algorithm is a little less straightforward but it can be shown logically that the algorithm metric reserve uses, will eventually bring everyone to equilibrium.
This problem of distributing reserves actually is closely related to another problem in digital currencies known as "payment routing". It is relevant to systems like ripplepay.com and bitcoin lightning network. It's been understood for some time that facilitating payments by routing through a social graph where shared credit or value exists is possible. The issue becomes when pondering this that each "routing" act changes the shape of the graph and requires further processing. Hence, the system will gravitate to where "hub" nodes are needed "clear" a payment. Metric reserve solves this problem the other way. To avoid hubs and central players everyone shares the risk, but also gets the benefit of more elastic monetization of value. It's easy to setup and easy to tear down. Though, admittedly it takes a while to see this economically. I struggled with it for a good 10 years.
One important point that needs to be clarified is this: This is a completely voluntary system. The algorithms simply provide information. They do not transfer money or make payments on your behalf. They simply inform the network of participants HOW to act. It's still up to each individual user to follow the protocol. Your connections are not obligated to connect, transfer reserves, or make payments to you just like you aren't towards them. Metric reserve is nothing more than a protocol and application for operating community-based person-to-person banking. It puts people and their connections in the drivers seat. It doesn't rely on a specific currency, or a centralized trusted entity. Anyone can operate it independently from others or as part of a network. It works the same wherever it's used.