Your question actually asks for the definition of inspiration. Pretty complex question, and if ever someone works out the science, they`ll become multi-trillionaires.
Ideas, in my opinion, are connections
. I believe that`s why the best way to generate ideas involve using a whiteboard and brainstorming session, or to use "mind mapping
I also think that every idea begins with an intent toward a goal, solution, destination, or accomplishment. It doesn`t matter what`s the goal, so long as there is one of some sort. Nor does it matter how vague that goal may be at first, as long as the focus is on the goal.
For example, the goal might be to save the planet from aliens. ALL discussion from there would be "how" to reach that goal. On the other hand, the goal might be to get an additional piece of pie without anyone knowing about it.
Ultimately, ideas are all about "how" something happens.
To come up with ideas for a business, it makes sense to first look at things you like or enjoy. Examine "how" they take place. Then take a look at whether you can perform that "how-ness" better, cheaper, or with higher quality.