Unlike atomic swaps — where LN needs to be enabled on both cryptocurrencies participating in an exchange — submarine swaps only need one side to be lightning enabled. ~Blocknomi - Submarine Swap
You want to pay something in the Lightning Network but don’t want to manually manage channels yourself. Submarine swaps allow you to use your on-chain bitcoins to pay the lightning invoice (through a swap provider).
Lightning merchant shares a secret (or hint?) with buyer. You pay swap provider over blockchain (via a HTLC), where the funds can only be locked with the secret. Swap provider will send money to merchant via lightning w/ the clause that the merchent needs to reveal the secret to claim the funds. Upon revealing, now the swap provider knows and can claim the buyer's money. while the swap provider claims the money on-chain, the merchants does it off-chain.
When a channel's supply of BTC runs out, there is no method to "refill" the channel, so another channel needs to be opened.
Submarine swaps provide a solution to this problem by allowing LN channels to be refilled through an on-chain transfer from the Bitcoin blockchain to the off-chain LN channel.