An algorithmic stablecoin is a stablecoin that tries to keep a fixed price, usually one US dollar, through rules written in a smart contract that create or destroy tokens as demand changes, instead of holding reserves of cash or bonds. The full explanation, with how these designs work and why several have failed, is on the Algorithmic Coin page.
The best-known failure is TerraUSD, which lost its peg in May 2022 and took its sister token LUNA down with it. Since then regulators have treated such designs with caution, and most large stablecoins are backed by reserves instead, as described under fiat-pegged cryptocurrency.