While in Inception, 2010, Sci-Fi Movie things slow down when you incept. But on the contrary, agile inceptions are more like creating the seed of a project. And they will in turn, turn into a systematic project development and production evolution plan, especially if you are not clear on what do you want, it makes sense to invest this time.
Many tried to paint a picture of inception like a bigbang and everything evolved from there, I personally don't agree with that - but a paper published in Agile XP as an experience report from Jonathan Rasmusson kind of summarizes this concept pretty nicely here. And in their elevator pitch they quote my favorite quote from Gordon Moore's "Crossing the Chasm" I am linking excerpts here, if you like it please go ahead and order it. So in short an inception is to distill the essense of project in following format
"For [target customer] who [statement of the need or opportunity] the [product name] is a [product category] that [key benefit, compelling reason to buy] unlike [primary competitive alternative] our product [statement of primary differentiation]"
This is pretty true for many co-founders or project managers, many a times I have faced product managers with rough outline but not a complete thought process around features and progressions for road maps. Apart from that you can cover few points which are not directly related, so the first thing is to create above statement which is your elevator pitch
We will many more things to cover, but having a elevator pitch is good start, usually rest of program is more around following things
If you are starting up or you have a new project around, it's always good to do inception, it works better and has it's own merits. I thought not to explain many things here, since the links I provided above cover almost everything