A pool is both the venue and the inventory. Depositors supply tokens, traders swap against them, and the contract enforces the pricing rule. Depth is simply how much is in the pool, and it determines the price-impact of any given trade size far more directly than on an order-book venue.
Pool composition is the risk. Supplying a volatile token against a stablecoin exposes you to the volatile token's full drawdown plus impermanent-loss; if the token is a scam, the pool is the exact place your capital is taken from, since a rug pull is usually the removal of the other side of the pool.
Before depositing, check who can withdraw what. Locked liquidity, verified contracts and a meaningful share held by parties other than the deployer are basic hygiene. See liquidity-lock and soft-rug for the failure modes.
Related: amm, lp-token, impermanent-loss, liquidity-lock