Curve is a decentralized exchange specialized in trading of highly correlated assets like stablecoins. It allows anyone to trade assets and provide liquidity to earn trading fees.
Curve launched with the goal of being an efficient fiat savings account for liquidity providers. To achieve this, the team at Curve designed the stableswap AMM algorithm which is a combination of the constant product (popularized by Uniswap) and constant sum formula. Trading occurs on a constant sum curve when the pool is relatively balanced and switches to a constant product curve when imbalanced. This allows for lower slippage and impermanent loss but is only applicable to similarly priced assets like stablecoins. The protocol charges a fee on every trade within a pool.
Curve makes money through protocol fees that are currently set at 0.04% for each swap with 50% going to liquidity providers and 50% to eligible CRV token holders (veCRV). The fees as well as pool parameters are decided by the Curve DAO or CRV holders.
You earn swap fees for providing liquidity on Curve. Each pool also provides incentives in the form of native protocol tokens and the CRV token, which represents voting power in the Curve DAO. You can also stake CRV (veCRV) to earn a portion of trading fees.