Bitcoin is a digital decentralized unstoppable form of money that you can buy, sell and exchange directly, without an intermediary like a bank. It uses peer-to-peer technology to operate with no central authority; managing transactions and the issuing of bitcoins is carried out collectively by the network. Bitcoin is open-source; its design is public, nobody owns or controls Bitcoin and everyone can take part. You can learn more on bitcoin.org.
The Lightning Network is a layer built on top of Bitcoin. It allows for faster payments by processing transactions away from the main blockchain - while keeping the same decentralization and security. You can learn more on lightning.network.
It looks like a regular email address (e.g. lightning@settleup.io) but you can send lightning payments to it. Normally if you want to send a lightning payment the recipient first has to generate an invoice which you then pay with your wallet. When you have a lightning address others can send payments to it anytime without you having to generate an invoice first. See more here.
In Settle Up you can settle your debts via the Lightning Network. The recipient needs to have a lightning address filled and you simply pay directly to it. No extra fees (other than the network fees), no involvement of Settle Up, you pay directly the person you owe.
There are many Lightning wallets you can choose from. There are 2 categories - custodial and non-custodial.