There is an objective world. It is out there and we inquire about it in terms of "what is...?" If you are a postmodernist and, henceforth, an antiscientific douche, please jump off a cliff now.
So, now that we're a bit lighter on the reader front, let's continue. As I was saying, there is an objective world out there. Views abound as to what are the parameters to grasp it but we can safely says that there seems to be, at this point in history, a consensus on how to measure it and catalogue it. Any doofus walking into a serious lab and demanding for kilograms, centimeters, and the like to be abandoned in favor of measurement in lollipops will be kindly escorted out by security. We have pretty much settled how to identify, classify, and measure chemicals, plants, animals, cells, rocks, light beams, sounds, and whatnot. It's all there, contained in pretty hardbound books which sell for serious cash up to the point when the new edition, revised with new discoveries and consensuses, hits the bookshelves.
The hard problem with this is that for you and I, common mortals, when we walk the streets and see a tree (ripe with hanging fruit, gently blanketed in pearls of tinkling rain drops, and its leaves producing something like a music when caressed by the morning breeze, all of it exuding a luscious fragrance) we are blasted by a fiesta of sensory experiences (sight, smell, sound, you name it) that evokes a thousand emotions, perceptions, ideas... and, my friend, to sum it up, that IS what life consists of, i.e. a collection of sensory experiences. Scientists have plugged cathodes on people's heads and stuff them into MRIs for long time, and know very well how light goes into the eye, how sound waves go through the hearing system, how the olfactory system processes scents, and how cells, neurons and that stuff lights up like a Christmas tree inside the brain with every sensory experience. That's not the problem. The problem is that none of that adds up to explain the rise of the blossoming, exotic and rich world of conscious experience. In summary, science knows how we experience at a physical level but it doesn't have much on what/how/why that makes us feel.
Philosophers call that gray zone the qualia, i.e. the qualitative aspect of experience or, to put it simpler, why it feels to us the way it does when the sensory experience is processed inwards. And this is like washing one's genitals, you know? It's really, really intimate, so we don't have a clue how and why that feels the way it does, and even less if it feels the same to the dude next door. So, faced with this conundrum, philosophers take one of three paths:
(a) to give up,
(b) to take the physicalist path and say that the little Christmas tree in the head is all there is to it and we shouldn't search for the tooth fairy, or
(c) to recognize that there are properties in the mind which are not physical though emanate from the Christmas tree happening in the brain, i.e. extra features of reality which remain unacknowledged by science.
But, why so much anal fixation for this? --you may ask. And your question would be well placed. Well, all this brouhaha and mental masturbation boils down to the human need to know, and there is something which still remains unknown and mysterious, and that thing is consciousness. We can venture saying that being conscious is having experiences which involve qualia but if qualia can't be explained then consciousness is conceptually shut down. There's a psychologist named Nicholas Humphrey who says that there is nothing beyond the physical and that the purpose of feeling that special thing which is called qualia has precisely the function of being mysterious so we all feel special about it and call it consciousness and do stuff with it, but without anything beyond the neurons and circuits in the head. That is a physicalist theory, but there are way more than that and, moreover, there are the dualist theories, which talk about both physical and metaphysical aspects, with some talking about physical aspects of the mind but in a correlation that creates the emergence of another level, non-physical, in which consciousness resides.
Me? Well, I'm a simple canine, but I'm seduced by the idea of the meta-mental. Hear me bark: when I, as a dog, fancy a treat, I just fancy the treat. My tummy has space for it, my mind has stored the smell of it, and I sense that there is one hidden out there for me. I want it. And I go for it, either by myself or by whining until I get it. Am I aware that I want a treat? Not really. I just want it. Human consciousness is like wanting a treat and being aware that one wants a treat. It is a meta-mental state. Awareness being the key word. Since we cannot capture with physicalist methods a non-physical propriety, then we have to go the abstract way. Then there's the issue of hard science. What has been observed in people who lack portions of the brain or have them damaged beyond repair, is that they are conscious not only of their body and the environment around them but also realize that they exist plus comprehend the awareness of their own existence. In cases of children with just the brain stem and cerebellum, it is not possible to measure if they're self-aware as they lack the capacity of language but what is undeniable is that they laugh and cry, to the point that at least the hint of consciousness is there.
It will take years, perhaps decades or centuries, to exhaust the physicalist approach to human consciousness. Maybe when that avenue is fully transited we will start entertaining new methods or new ways of thinking, all in search for things we don't know and which make humans what they are. So far, we know that, indeed, there's something there which blossoms as an organism develops a more complex mind, and which is both a blessing and a curse. Trust me on this one: wanting a treat and getting it, with no mental masturbation involved, is a way simpler, more satisfying existence.