In general, being "fat adapted" means that your body is able to efficiently utilize fat (either endogenous or exogenous) as a fuel source.

This is usually offered as an alternative to being a "sugar burner" whose body is accustomed to having a regular supply of glucose (typically from dietary sources, a la "eat every three hours").

Generally, one is considered to be "fat adapted" when they can go without eating without discomfort or adverse symptoms for several hours at a stretch, allowing for the so-called Intermittent Fast.

Here is a pretty extensive MDA post on the subject... http://www.marksdailyapple.com/a-metabolic-paradigm-shift-fat-carbs-human-body-metabolism/#axzz1wBxJskQY

If it helps to visualize what is going on, here is a model of cell bioenergetics...

This might also be helpful...

The energy used is not only determined by diet (i.e. "low-carb" vs "moderate/high carb") but by the type of activity one engages in (http://www.sciencedaily.com/releases/2007/06/070618124541.htm) as this places varying demands on the body's energy systems.

I think that the "fat adapted" vs "sugar burner" analogy is reductive and simplistic. The actual process is much more complex and subject to a high level of individual variation. However, the SAID principle (http://en.wikipedia.org/wiki/SAID_principle) does come to mind and by changing the "demand" (by eating more or less carbohydrates for example) you will stimulate a physiological adaptation that seeks to adjust in order to maintain homeostasis.