Connor, the meaning is contained in the word order. "Nous aimons tous les chats" means "we love all the cats." To say "we all love cats," you would switch the order of "tous" and "aimons," so that the phrase reads as follows: "nous tous aimons les chats."

I agree with Benjamin, it all depends on how "tous" is pronounced. See this post about the subject -> https://www.italki.com/question/371036 In written form, it is a contextual guess, though I would favor [we all love cats] as my primary choice. And if this was : nous aimons tous les fromages probably my primary choice would be [we love all kind of cheeses]. This is motivated by the variety : while cats can be seen as homogeneous, cheeses are numerous, so the choice reflects that, but again this is only the primary guess, another context could lead to the opposite choice, for instance if you work in a pet shop.