The feelings of being hungry and feeling full after eating differ from person to person, so the human body has some explaining to do. Every physical feeling is caused by chemistry, whether it be a reaction or an imbalance in the system. When studying eating and the human body's relationship to food, you must look at the two steps—your body compelling you to eat, and then your body telling you that you've had enough food (why you feel full after eating).
There's a physical reason a person feels hungry—it's triggered by a lack of glucose in the blood. This depletion sends signals to the liver and brain that, essentially, cue a high alert state, and the hormone ghrelin signals the brain to say "feed me". Evolution has covered the "eat, eat, eat" part of the digestive process, but it doesn't do so great covering the "stop, stop, stop" part. Luckily, there's also a physical reason why a person might be feeling full after eating—what scientists call "satiety signals".
What are "satiety signals"?
Satiety is the feeling of fullness a person experiences after eating that suppresses the urge to eat for a period of time. Fullness can begin as early as when a food or drink is consumed, and it continues as the food enters the gut to be digested and absorbed.
With that process, the stomach expands to accommodate the meal, causing satiety signals in the brain to go off. These hormonal signals are a response to the digestion and absorption of nutrients, but others, named leptin, tell the brain how much fat is stored in the body. Both signals are involved in long-term satiety (a person with more fat needs less food to satiate their appetite) and energy intake.
With so much communication from the stomach to the brain and then to the digestive system, there's some lag from when a person first starts eating to finally feeling full. Thus, eating slowly so your body has more time to process and get back to you prevents you from overeating.
Do obese people have differences in certain hormones, leaving them prone to feeling less full after eating?
As leptin is the hormone that controls hunger depending on how much fat a person holds on their body, you'd think obese people have lower leptin levels. BUT surprisingly that's not the case (science is so cool). They actually have high leptin levels, but the hormone isn't able to do its job because their brains have become desensitized to it.
What are the leptin levels for when you're thin and trying to lose weight?
Also another interesting point—the thinner you are, the lower your leptin levels drop, and the more food it takes to satisfy your appetite. Your body always tries to regulate itself and keep you healthy; when extremes on either side approach, the body reacts chemically to get you back to normal.
And that's how it works! The most important thing for you to do is listen to your body. When ghrelin tells you to eat because you're hungry, eat. When leptin tells you to stop because you're feeling full after eating, put down the spoon (or sneak in another bite, no one will even notice).