The definition phase is a fancier, and maybe ambiguous terms for what is commonly labeled as the design phase. However, I don't want to label it as such, since I think it the term design limits the application in many minds.
So...at the beginning of the definition phase, you have an idea of what you would like to accomplish, but the idea has so many paths at this point, that you haven't determined the scope required to execute it.
There are two ways you can work through the definition phase, and I liken this to the software development design processes (waterfall vs. iterative).
Iterative Definitions are like seasoning the pan. You design a little, then you build a little. Waterfall Definitions are where you define everything upfront, and then move to the execution phase.
Note that there is no definition style that works for every idea. Sometimes defining everything upfront makes more sense than doing it in smaller pieces. Also, you can start with a waterfall type approach, and as the definition matures move into a more iterative approach.
The execution phase is not dependent on the definition phase. However, you continue at your own peril, since not going through the design phase can have you wondering in the wilderness during the execution phase.
As I have said, the definition phase is not limited to the label of desigining based on its mainstream use. Technically, when you decide to go on a diet, it would be a benefit to you to design the structure of the diet. For example, what meals are you going to eat, or what feeding schedule will be used?
The diet example illustrates that you can use the waterfall approach in the beginning, and then move to a iterative approach to correct things that aren't working for you.