According to the Oxford dictionary, the word is defined as:
'the establishment or starting point of an institution or activity'The word is also loosely used to mean 'beginning', but the movie takes this basic English meaning and migrates the action part of it to an idea. So now it means:
'the act of implanting an idea in a person's mind'Since the language defines 'inception' differently, this makes the term specific to this movie and therefore part of its jargon. You will notice that most of the jargons used are derived from Latin including 'limbo', 'extraction' and 'projection'. Like most sci-fi comics and movies, the words need to be of Latin descent to sound scientific and sophisticated. When done right, this aids our suspension of disbelief sufficiently.
One of the reasons I like the word is that it sounds simple, rolls easily off the tongue but still retains a certain mystery. It's not a word that everyone knows, but yet one that is not restricted to high literature. It has very little of the obvious flashiness of 'The Matrix' and plays a central role in the backstory as well as the plot.
This appeal is enhanced by the movie itself. The trailers did a very good job of explaining the term, without giving away the story, unlike most trailers today. I don't know if Christopher Nolan spent a lot of time thinking of the right word, but it's likely that he had a Eureka moment when he thought of the word.
One thing is for sure: 'Inception' by any other name would be as sweet.
P.S: Also check out, 'Writing English as a second language', by William Zinsser for more on Anglo-Saxon and Latin words.