It’s their informal name for themselves, The Piss Club, an expression adopted from the humaverse because the floof think it’s so funny. (Do humans really think that animals are so interested in that aspect of their business? See how funny it is?)
The Piss Club’s formal name eludes translation from floofish. For humans (and the animals involved), The Piss Club is about ensuring that animals (or their allies) are present whenever humans do their business. In homes with pets, this is generally easily accomplished. Public facilities can be handled via rats, birds, flies, mice, spiders, etc.
Those places are not the problem, and it’s not about humans doing their business. It’s about verifying what they are.
No, the problem is those private places where pets don’t reside, where spiders and insects are stalked and killed, and mice are treated like vermin. Those places are the problem, because those people might be the beings that The Piss Club are supposed to on guard against. Masquerading as humans, those beings could destroy Earth; it is their stated intention, and they are here on Earth.
And, while floofs (except for dinosaurs) usually originated on other worlds (or other universes, in frequent cases) (funny how two beings, say two cats, can look so much alike and yet be from different universes) and arrived on Earth to expand their influence (and study other cultures and life forms), they’ve grown fond of those crazy creatures called humans, and would like to keep them around. Because, as the floofs have found, humans don’t exist anywhere else in any other universe (unlike dinosaurs, which seem to be everywhere), making humans very unique creatures.
That’s why The Piss Club watches.