xSigma at its core is a stablecoin exchange.
How it works is that there is a special smart contract that holds a pool of three stablecoins: DAI, USDC, USDT. You may find this contract at this address: 0x3333333ACdEdBbC9Ad7bda0876e60714195681c5.
When someone uses xSigma to exchange stablecoins, they send a certain amount TO an xSigma smart contract, which calculates the current exchange rate, and the person receives the corresponding amount in the output currency FROM the smart contract, minus a small fee.
This way, under normal operation, stablecoins never leave the pool, ensuring the safey of LPs' assets. The proportions of the stablecoins may change, but the total amount always stays the same or grows slightly in line with the fee amount.
The pricing algorithm that calculates the exchange rate ensures that the stablecoins are balanced. When there's a shortage of a coin, its price becomes higher, providing an arbitrage opportunity for anyone to re-balance the pool. This is an example of a StableSwap algorithm presented in the following paper: https://www.curve.fi/stableswap-paper.pdf.
Simply put, the stablecoins of LPs are used as liquidity for trades on the exchange. If someone wants to exchange $1000 worth of USDT to USDC, we'd need to have ~$1000 worth of USDC accordingly, so we need enough reserves to execute the exchange, which is where LPs with their stablecoins come in.