There are a few different ways that faucet owners make money. The first is through advertisements. Many faucets will have banner ads or pop-ups that generate revenue for the owner whenever someone clicks on them.
Another way faucet owners make money is by collecting fees from users. Some faucets require users to pay a small fee in order to withdraw their earnings, and this can add up to a tidy sum over time.
Finally, some faucet owners simply sell the Bitcoin they've collected from users. This is probably the most common method, as it's easy to convert BTC into cash via online exchanges or local buyers.