It’s exactly what it sounds like. Extra bullshit monthly rent tacked onto the regular rent in addition to a usually non-refundable pet deposit at time of move in or pet adoption.
Basically you’re a money faucet in the US, and wide open if you have pets or kids
To be clear, rent is usually one value for however many humans will be living there, but everywhere has different rules for pets. For the most part you’re restricted to one or two dogs specifically if they’re allowed at all. Some places will charge the same for one or more, some will charge more for 2. It’s really variable. But with RealPage leading the way with the largest rental management companies, is getting pretty unified and difficult to not get fucked over by.
Smaller pets like fish or hamsters usually aren’t mentioned or charged for though that I’ve seen.