Basic liquidity pools such as those used by Uniswap use a constant product market maker algorithm that makes sure that the product of the quantities of the 2 supplied tokens always remains the same. On top of that, because of the algorithm, a pool can always provide liquidity, no matter how large a trade is. The main reason for this is that the algorithm asymptotically increases the price of the token as the desired quantity increases. The math behind the constant product market maker is pretty interesting, but to make sure this article is not too long, I’ll save it for another time.

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The main takeaway here is that the ratio of the tokens in the pool dictates the price, so if someone, let’s say, buys ETH from a DAI/ETH pool they reduce the supply of ETH and add the supply of DAI which results in an increase in the price of ETH and a decrease in the price of DAI.
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How much the price moves depends on the size of the trade, in proportion to the size of the pool. The bigger the pool is in comparison to a trade, the lesser the price impact a.k.a slippage occurs, so large pools can accommodate bigger trades without moving the price too much.