How is an idea born? For you, what is inspiration?
I like to keep things by the definition. Too many things in life have been distorted by everyone's personalised or twisted-by-pop-culture references. ANYTHING can be an inspiration. The sense of inspiration is obviously the uplifting experience of being inspired. It might not take an outside influence for someone to be inspired - I know I've gotten great ideas 'Inspired' by a memory of something I did or said.
Point is, "What is inspiration" isn't really the issue. "What is it that inspires in particular," is what's relative to everyone.
As for the idea, it's 'born' the same as any thought or putting two and two together. Some ideas are thought out complexly, other are very simple. Apart from that, they are simple the result of someone's mind. It's relative on whether someone constructs upon these ideas or are prone to immense creativity.
For me, I just take it as it comes. I get an idea - I think it out. Many times I like to use the term "Brain Fart".