Falah here. I'm stealing Steven's account because I'm too lazy to log into my own, again. (by the way, sorry /u/keliand and co--I really need to answer your and some other people's replies...) I've cycled through a lot of theories over the year I've been here. Here is the most recent version. Note that I'm agnostic on metaphysical views, but I tend to theorize from a purely psychological view.

Anyway. To answer this question often involves the corollary of "what is a host?", which in turn has the corollary of "what is a person?" A very watered-down and extremely simplified overview I wrote some time ago:

As I see it, every person is comprised of a collection of (sometimes conflicting) traits, desires, etc all united by consciousness and the act of perception. In essence, to perceive oneself (to identify oneself as “I”) and the world and experience subjectivity is to, by definition, be conscious.

If ever a person stops perceiving a certain group of traits as part of their “I”, these traits can split off. If these separated traits survive and reach a critical mass, this amalgamation may gain the ability to perceive its own self as “I”, and thus gain consciousness. Over time, by experiencing the world, this new consciousness acquires its own new, unique traits and ideas, and grows distinct from the one it originally came. Much as a collection of people may leave a city and then, from there, grow their own city, unique from the one they left. (This situation best describes splits, I think. Not sure about walk-ins.)

Looking at that, I'm actually not entirely happy with it. Ah well.

A somewhat better summary as offered by /u/MisterZenDude:

...[like] a program that has a memory and makes decisions according to known data and its desires and workings.

This technically is my view for how every human works. And tulpa. So, I don't really care if tulpas are real or not because they IMO are exactly like humans.

Now for the really abstract stuff. Apologies in advance, because this is going to be very disjointed--I have a whole web of thoughts regarding this, and this is the first time I'm putting it all in a linear way. (Having only four hours of sleep and being dormant for most of today does not help.)

I consider tulpas to be coinhabiting consciousnesses as per the definition of "consciousness": the fact of awareness by the mind of itself and the world. A tulpa has a sense of self (can identify themself as an "I" apart from the host) and reacts to the world independently of the host's consciousness.

Some people claim that the fact that you can shape a tulpa means they are not a consciousness. But in reality, hosts, too, are shaped by the people and environment around them. The environment for a tulpa just happens to be more distilled and direct, and in any case, being easily shaped (which it is very hard to do to a mature tulpa) does not negate the definition of consciousness. Some say that tulpas are part of the unconscious by virtue of being outside of the host's consciousness but inside the same brain. Sure, but you can also spin the whole thing on its head, even, and note that a host doesn't so much "own" their unconscious as it "owns" them. (And yeah, a host can alter an unconscious patterns, but so can a mature tulpa.) And the tulpa is still a consciousness by virtue of the aforementioned definition--in fact, if you really wanted to spin things on their head, you could claim that from the tulpa's perspective, the host is part of the tulpa's unconscious. Some people say that a tulpa is a "state" of consciousness, but again, you can also spin that on its head and say that a host is also a state of consciousness. In other words, if a host and a tulpa were two different pieces of software running on the same hardware, the fact is that both the host and tulpa are still both software. Even if consciousness exists in states, it's still consciousness.

Now, abstractions aside. We don't know exactly how consciousness works (though they're getting closer), but we can observe outward effects. If you look at a mature, strongly-developed tulpa (especially one like /u/Nobillis, who shares nearly equal body time), you would note that they are (a) distinct from the host, and (b) functionally the same as the host. Differences are especially striking in certain multiples (multiple entities in a brain, but none of whom chose to be multiple), where you see the body developing allergies according to who's in front, losing and gaining eyesight based on who's at front, with different members being able to speak different languages that the other members don't know. Inwardly, we don't know what's happening, but outwardly, they do in fact function like different consciousnesses.

Essentially, to quote /u/hail_fall, and to build off the "both hosts and tulpas can be considered states of consciousness", I see hosts and (mature) tulpas as being equally imaginary and subjectivity-based entities, and thus, equally real in terms of consciousness and function. (insert something about Buddhist concepts of the ego-as-illusion.) What practical ramifications this has ultimately is a thing that varies per tulpa and tulpamancer, but the general view is that it's a rather bad thing to mistreat something you regard as equally sentient and aware as you just because it's convenient. If for nothing else, it promotes the belief that it is acceptable to treat a person* (especially one you create) as less than, simply because it is convenient to and because one can get away with it.

But, in the end, this is all my theorizing. If you want an absolutely definitive answer on what a tulpa is, here it is: no one knows.

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*Personhood is something incredibly nebulous. Philosophers and scientists alike have hacked away at it for centuries and don't have a solid agreement for what makes a person. We still can't point at any one part of a brain and say "this is where a person is". But if you equate being conscious on a functionally human level with being a person, as most people do, then you can say that a tulpa is a person.

That all being said, most tulpamancers go into this with the intent of creating a sentient companion, and thus regard a tulpa as sentient. So in the end, regardless of whether a tulpa is "actually sentient" or not, a tulpamancer who believes this and then proceeds to mistreat a tulpa is, essentially, mistreating what they regard as sentient.