Submarine Swaps are a way to trustlessly move bitcoin from your lightning balance to the onchain ("normal bitcoin") balance (or reverse) without opening or closing channels.

So essentially you can send from lightning to an onchain address or reverse.

Swaps require a counterparty (that does the opposite of your swap, e.g. you send on lightning, the counterparty receives lightning and sends you onchain bitcoin), this is usually a company providing this as a service (e.g. Boltz). Electrum now instead allows anyone to become this counterparty and announce their server on Nostr. This creates a market for swap providers. Regular Electrum users then can see these servers in the wallet, choose the cheapest one and swap with them.

Why would you run a swap server? Mostly to earn fees.

Why would you do swaps as a normal wallet user? For example to move liquidity to the other side of your channel, so you can receive incoming payments again. You could also try to obfuscate your onchain history (increase the privacy of your bitcoin), by opening channels and swapping out of them again, so the link of your transaction history is broken on chain.

Not exactly sure how Muun wallet works, but iiuc in muun you only have a onchain balance and if you pay a lightning invoice its a swap :? Also Muun has no marketplace for swap providers, so you can only swap with them and have to pay their fee.

In Electrum you can open lightning channels, and as a result you have a separate onchain and lightning balance. And if you want to move sats between lightning and onchain you can either open/close channels or do a swap (with a counterparty you can discover via nostr and choose the cheapest or e.g. most reputable from).