So Inception is basically about a man, DiCaprio, who's really good at going into people's dreams to steal information (extract) from their subconscious. The whole plot of the movie was about some corporation, Watanabe's, hiring DiCaprio to plant an idea into a rival corporation's subconscious, rather than extracting it; this is called inception. In order to plant an idea into someone's subconscious though, you'd have to go a couple layers down into a dream, a dream within a dream.

They mention a couple of key points throughout the movie, such as you have to die or feel a kick (freefall) in order to wake up from your dream. Also, each dreamer usually keeps a totem with them, which is an item only they know the properties of, so that they can always tell whether or not they're dreaming.

DiCaprio assembles a team, and they actually go several levels down within their dream. Level 1 is the van and bridge. Level 2 is the hotel. Level 3 is the snow fortress...where Murphy (rival corporation's heir) was supposed to think of the idea himself. However, they went into limbo too when DiCaprio's wife kills Murphy.

Anyways, I'm not so great at summarizing, so please just check out the best source on the internet, Wikipedia: Inception. Basically, the film is open to two different endings.

The totem falls: DiCaprio's wife is really dead and he reunites with his family.

The totem keeps spinning: DiCaprio is still in a dream, his wife woke up by jumping off the building, and she's trying to wake him up by going into his dream and trying to spoil everything. Remember, DiCaprio never had his own totem. This also means that everything was a dream. Watanabe hiring him, his entire team, everyone is just his projection. I think I prefer this ending, but it is still kind of sad to think that he's stuck in a dream.