Think of where you're sitting now. Besides just being aware of the room you're in, or the chair you're on top of, you have access to years of biologically stored pathways of information that maps sensory motions, experiences, feelings, and memories. All of this previous information, makes you, well you! You may be conscious of it now, but how long has your consciousness lasted? How inexorably tied are you to the matter in your body?
Think back to one of the earliest memories you have. It could be that you remember life as a child, or if you have an exceptional memory you might even remember your infancy. The funniest part of that memory is that you actually weren't there. All (or nearly all) of your body's atoms were not the same back then. They have since been changed or replaced by metabolic processes and years of taking in nutrients and expelling waste products. It gives us the notion that consciousness does not lie in the realm of atoms, but some higher construct of cells. In a broad sense however, consciousness is the continuation of sensory input, and the ability to create new memories.
Have you ever been put under for a surgery? On one occasion around my 16th year, I had to have my wisdom teeth pulled. The most fascinating event of my life so far was about to happen: I was about to experience a state of total anesthesia. I remember lying back in the dentists chair, and they had just inserted an I.V. into my arm. They told me to count back from 10, so I did, completely convinced that I would get to negative 3. I felt slightly anxious, and every one of my senses was on edge. 10...9...8...7... At around seven, it suddenly dawned on me that it was probably a better idea to say the words in my head. I thought, 6...5... I lost interest in counting at all. My senses were waning. It wasn't so sudden, it was more like a gradual slide into oblivion. I progressively noticed less and less about the world around me. When seconds before, I was alert, and tense, and anxious, now I couldn't have a care in the world, and I couldn't even recall why. Then, I felt a numbness in my mouth. I opened my eyes and it took me about a minute to realize it, but I figured out it was over. Over two hours had passed since my last memory. My chain of consciousness was telling me I was sitting in a chair one moment, and literally the next moment I was lying down in a post-op room. There was no sensation of time in between those two events, it was nothingness. I existed for an entire 2 hours without even knowing it. I couldn't recall any memories during that time, I couldn't make any new memories during that time, but still I was THERE. I was enthralled by that idea, where did my consciousness go? More important questions would lead me to ask, what makes me, me?
Imagine for a minute that I give you a whiff of chloroform, the last thing you remember before you pass out, is succumbing to a desire to sleep. While you're passed out, imagine that I clone you in adult form, atom for atom. (If I let the both of you live, it's easy to see that you are each separate beings. You and your clone would probably have the exact same reaction to seeing each other upon waking up, but slowly, as different independent experiences change your mental states, it would dawn on you that you guys are in fact, separate people.) In this scenario however, just to make things interesting, I'll kill you. Your clone will wake up from a chloroform induced haze with all of your memories, experiences, and (assuming I don't say anything) it will never even know its a clone. Your clone will keep on living your life exactly as you would have, and he or she would never know the difference. Meanwhile you are in fact dead, but an exact copy of your consciousness lives on. Your own consciousness is gone, never to see the light of day again. Most importantly, how could your copied consciousness tell if it was a clone? It couldn't! Your copy would have the memory of passing out from chloroform, things getting hazy, then things getting clear again and waking up: A complete connected steam of events.
Imagine for a minute that you step into a futuristic particle separator. It uses advanced electrical repulsion fields to momentarily separate every atom in your body, then it puts every single atom back in the place that it already was. Sitting inside, you would hear the machine turn on, your would feel a numbing sensation as nerves and tissue begin to be separated, and then? Nothing, no consciousness. Assume for a second that your atoms never got put back together, what would happen to your consciousness then? Common sense says that you wouldn't feel anything at all, nor would you ever feel anything again. It's the equivalent of death. But say we do put your atoms back in place. Who's to say that you are inexorably tied to your atoms, and your own original consciousness (once destroyed) would come back into being? The matter that was reassembled would be conscious of course. It would even have the memory of stepping into the separator, momentarily losing consciousness, and then coming back. The funny part is, it would have no way of distinguishing whether or not its own consciousness was continuous. Whether the original was destroyed, or continuous, both scenarios are remembered the same way from the re-assembled person's perspective.
One more quick example with teleportation. Basically it's the same concept. A weird phenomenon called Quantum entanglement now lets scientists teleport simple things like photons, atoms, and clusters of atoms. Theoretically in principle it can do the same with humans. A futuristic teleporter then, would disassemble and effectively destroy anything that goes into it. It would "read" the information put into it, and assemble an exact copy in another location. From a bird's eye perspective of the whole thing, it looks like simple teleportation. Something goes in one door, comes out the other door. But factor consciousness into the equation. Hypothetical example: Dr. Jones, the eccentric scientist who invents teleportation, volunteers himself to be the first human to try it. He steps into the first teleportation door, and is destroyed. An exact copy of himself emerges from the second teleportation door, and the first words out of his mouth are "Eureka, it works!" From the copy's perspective, he retains the memory of walking into the door and now has the experience of walking out of another door in a perfect linear stream of consciousness. But from the original Dr. Jones perspective, he walked into the first door, and never had another thought again as he was destroyed. No awareness, no sensation, nothing...his consciousness doesn't even know he doesn't exist. Once again, the funny part is that Dr. Jones's copy has no way of telling whether or not he's the same person as the one who walked in.
In summary, its pretty hard to imagine what life is like without consciousness. Sometimes we have the ability to sift through our memories without taking in new sensory information, it's called dreaming. Some poor unfortunate souls have the suffered brain damage to give them the reverse. The are able to take in sensations and react to them, but they are unable to create any new memories. They are effectively trapped in a particular mindset forever. On some rare occasions during life, we lose BOTH our ability to make memories and our ability to sense. Ever had a really deep, dreamless sleep where time flew by almost instantaneously? Ever been knocked out cold? When we lose both of these key conscious indicators, a funny thing happens: its like we die. Our existence is moot, a thousand years could pass us by and we wouldn't even know it. We might never regain consciousness again and we still wouldn't even know it.
The scary part is, imagine that every time you go to sleep, your stream of consciousness dies in this very way. Every time you wake up again, some other manifestation of consciousness resumes your life with all your previous memories intact. The person who wakes up wouldn't even know that they are a replacement, they would go to bed willingly each night expecting to wake up, when in reality they die forever. You could be in this situation right now, the best part is, you would have no way of knowing whether or not YOU were really there in all the memories of the past, because they're simply that: just memories. Perhaps they're just some other conscious being's memories, stored in a biological matrix of nerves and tissue, and you're the latest inheritor to manifest from them. From a bird's eye view, our lives seem completely continuous, but can we ever know if they're not? Nope.
Just something to think about...sweet dreams.