Yes, it's a linguistics term. Animate things are perceived as having human-like agency. Many languages have a grammatical category clustering things like large non-human animals, the weather, or fire, or trees, together with humans. Animate. Everything else is inanimate and presumably less alive.

In English, many animals are referred to with "he" or "she". Being a mammal, large, being domesticated, being familiar, are all more likely to be animate rather than inanimate. A pet mare is going to be "she". Insects are always "it". Livestock or a reptile might get either. Babies sometimes get treated as inanimate. ("Is it a boy or girl?")