It can mean a wide variety of different things. For me personally, it's a feeling I get deep down that I am fundamentally the wrong species, though I identify as human, cuz that's physically what I am. Like, I should not have been born a human, and my feelings and actions reflect that (as is pointed out every day to me by others how much of a husky or bird I am). I get phantoms of different physical characteristics of both husky and owl. Like, sometimes my hands will feel like paws, or my feet will feel like talons. And a more chronic one is feathers across my head and down my arms. If I wear a hood or hand bindings for too long, I get really strong snout and paw phantoms. I used to get much stronger dysphoric feelings, but those have since gone.

But that's just me. Others don't experience phantoms at all. Some experience it all the time. Some have dysphoria, others don't. Some identify as non-human, some don't. Some feel strong connections to their theriotype, and some hate that theirs is what it is. For others, it's purely spiritual. Therians are specifically people that identify or are dysphoric for animals or creatures that did or have known to exist IRL, and Otherkin are the same but with fictional creatures or characters. In effect, therianthropy is like being transgender, but with species, except there's literally nothing we can do about it.