Inception isn't just a name of a movie; it's a word. According to good ol' Merriam Webster it means, "an act, process, or instance of beginning."
Sounds simple enough, but what does it mean in context? The point of extraction is to steal information from a subject, or mark, whereas the point of inception is to plant an idea in his or her head. However, like any plant (you can't just throw some seeds on the asphalt and expect an orchard) an idea needs to be cultivated.
That's what Eames teaches us and where the title of the movie comes from. It's not enough to tell Fischer, "Hey, Fincher: break up your father's company." It's an idea he needs to form himself.
The trick is to start at the inception, or origin of the idea and then let it grow naturally in the person's mind. Inception implies layers of mental depth, something deep within our mind that comes to us from nowhere, like inspiration or epiphany. This is what Cobb and his team seeks to do.
Dreams are (normally) formed from our own subconscious and so by simulating Fischer's subconscious, they can dive in and insert an idea that he will assume is his own even though its inception was actually in Saito's mind.