What is the Lightning Network, and why can it enable payments in seconds?
Amounts on the Lightning Network can be as small as one-thousandth of a satoshi (a millisatoshi). Its technical specifications are called BOLT. Segregated Witness (SegWit) fixed the transaction malleability problem, an important prerequisite for the Lightning Network to work reliably.
How much a channel can send depends on how the balance is distributed between its two sides. A large payment may fail if no route has enough capacity.
The value circulating on the Lightning Network is also $BTC ; it’s just that most payments don’t need to be recorded on-chain one by one.