If you only have time to read one paragraph, here’s the short version:

With Lightning, we can take sats “off-chain” into a Lightning channel. Users can route Lightning payments through a network of channels, and take their sats back “on-chain” at any time. Of course, the sats never really leave the chain, but the system works through some cryptographic slight-of-hand. Lightning is fast, cheap, and secure. Privacy is better than normal Bitcoin transactions, but still not perfect. With eCash, users can withdraw their sats “offline” entirely. Once offline, they can be transferred any way you please. You could send them over email or SMS. You could print them out in a QR code and pass them along in person. The possibilities are endless. The recipient can deposit the sats back “online” as soon as they receive the eCash, and withdraw them directly into any Lightning wallet. There does not need to be any traceable connection between the two parties to a transaction, which means that privacy can be very robust. There is one catch, of course: after receipt of the eCash and before depositing them back “online” to the Lightning network, the recipient needs to trust a third party server, called a mint. For that reason, taking received eCash back online should be done before providing any goods or services in exchange.