Inception is the allegedly impossible task of implanting an idea in someone's mind via dream-sharing and making them think it is their own. However, as the movie progresses, it is proven that Inception is not impossible and has, in fact, been done successfully twice (both times by Dom Cobb).
Nonetheless, inception is a very difficult process. It requires dreamers to plant the idea in a dangerously deep layer of the Subject. This becomes the first difficulty of inception, as descending into a level so deep (three layers or more) creates highly unstable dream level. A way to solve the problem with unstable dreams is to use highly powerful sedatives, but such a powerful sedative makes escape by death in a dream impossible. Instead, death drops the dreamer in Limbo.
Another necessary component in inception is to have the Subject accept the idea with as little involvement from the dreamers as possible in presenting the idea to ensure the Subject cannot trace the origin of the idea. Part of this is to make the idea as simple and as personal as possible to ensure the idea remains. Emotionally-based reasons for the idea are generally used if the idea is one that the Subject would not accept in real life, as emotion trumps reason in human beings.