When looking at the relationship between dreams and reality in the movie, the interesting question is not so much how dreams and dreaming works. (Which is for the most part simply one of science.) The interesting question is how fiction works, especially the sort of science fiction employed in the movie, which itself uses concepts such as 'reality' to create its own peculiar fictional world.
There's reality, there are dreams, and there's fiction. Within fiction (e.g. in the specific form of a movie), there is a projection of reality, with some features left as they are in reality, and others changed or removed. We can learn a lot by looking at what exactly the author of the fiction has changed, and why. In other words, what's interesting is how, and with what intentions, the author changed the material that came from the real world when constructing a fictional world. (Sidenote: what I've described for fiction here applies more generally to forms of unreality, not just fiction; however, when we generalize this, we must take into account that then not always a deliberate authorship is part of the process.)
1. Any sort of fiction happens in its own world, a world that has been made up from elements of the real world. Sometimes, what an author wants is to illustrate some point from the real world. For instance, if I make up a story in which a character is a notorious liar, and I construct the plot in a way that lets this liar get into more and more problematic situations, I illustrate the social effects of dishonesty and deceptiveness. Although the character and the events in the story are fictional, what I want to illustrate is the dynamics of social interaction, and the impact of a certain behavior (lying) on it, and the latter is something which is shared by the real world and the fictional world. As long as I keep up this parallel (and make it clear to the audience that in this respect, the fictional world is intentionally like the real world), my fictional world could differ in almost any other respect from reality. I might bend the laws of physics, for example; in this case, we'd have a science fiction story that happens in a world very different from our own, but it still shares the same social dynamics.
I'm thinking of much of the Star Trek TV series' here; although there was much playing around with concepts from science and technology, social aspects of its world were frequently just thinly disguised aspects of the contemporary world around it, sometimes up to the point of painfully obvious moralizing.
2. Sometimes, on the other hand, the goal of the author is not so much to illustrate something from the real world, but to emphasize an interesting possibility how the real world might have been different. (A possibility that can often only be exploited in fiction, at least initially; it may inspire some serious technological invention which makes it a reality later on.) Constructing the fictional world then rather takes the form of an "imagine what would be the case if ...". Such a deliberately built-in difference from features of the real world can be very gentle, and sometimes authors take a lot of effort to have their characters 'explain' it to us, in order to earn the audience's belief in that differing feature of their world.
As an example, take H.G. Wells' The Time Machine, the novel which first introduced the idea of time travel. It begins with a long lecture about the nature of space and time which has the goal of making us familiar with this imaginative idea; only then it starts exploiting this new possibility in its fictional world to demonstrate something about the long-term development societies may have to expect, by having the timetraveler going there and witnessing it.
In contrast, the difference between fiction and reality can also be brutally direct, without much regard for the irritation both the characters and the audience might experience about the divergence.
A case in point is Kafka's Die Verwandlung (Metamorphosis). In the beginning of that story, the main character is suddenly and without any direct explanation or motivation transformed into a giant insect, something which wouldn't happen in the real world. After the initial shock, however, that story rolls out the consequences of that situation without any further fictional device; it develops in the way one would probably expect things to develop, once the initial situation would be accepted. (I've elsewhere discussed that particular trick under the name of locally restricted fictionality).
3. Finally, constructing a fiction from elements of the real world can use the idea of contrasting reality and unreality itself; this is what happens when a play-in-a-play is part of drama, a character tells a story within a novel, a television show is watched in a movie, or a fictional character dreams. All these, of course, are small and simple examples. Compared to this, the contrast between reality and unreality might be made into a big theme that creates the framework for the entire fiction. This is what happens in movies such as Inception, and that's why reflecting on the particular way such films present the contrast between dream and reality is so interesting for learning about the way fiction works. (Note, however, that it is hardly a new and original genre just by itself; there's a long tradition here: just think of Shakespeare's A Midsummer Night's Dream.)