The "meat" is the gelatinous stuff. Me personally, I don't really dig it alone, but added to a smoothie or used to make some kind of pudding or soup or dressing, it's so sublime! My favorite smoothie is the water and meat from half of one, and some pineapple. It's a raw pina colada!
Yes, the water and the meat have that metabolism-increasing quality, as does raw coconut oil. I don't understand exactly how it works, but the fat in the coconut, which your body uses as carbs instead of fat, increases your body heat. The coconut oil forum here has some good posts about it, and more of a technical explanation ;)
So to eat the meat, you just scoop it out with a spoon. I don't like the consistency - it's too mushy, which is why I like adding it to things.