The easiest way to understand Curve is to see it as an exchange. Its main goal is to let users and other decentralised protocols exchange stablecoins (DAI to USDC for example) through it with low fees and low slippage. Unlike exchanges out there that match a buyer and a seller, the behaviour of Curve is different, it uses liquidity pools like Uniswap. To achieve this, Curve needs liquidity (tokens) which is rewarded by those who provide it.
Stable coins have become an inherent part of cryptocurrency for a long time but they now come in many different flavours (DAI, TUSD, sUSD, bUSD, USDC and so on) which means there is a much bigger need for crypto users to move from a stable coin to another. Centralised exchanges tend to have high fees which are problematic for those trying to move from a stable coin to another. As a result, Curve.fi has become the best place to exchange stable coins because of its low fees and low slippage. Every time someone makes a trade on Curve.fi, liquidity providers (people who have deposited funds onto Curve) get a small fee split evenly between all providers, this is why you will see high APRs on days with high volume and high volatility.