It works because there is a lag in the time you are satiated to the time your stomach tells your brain you are satiated.
People consume far more calories than they really need, very early in a meal. Many, if not most people, will eat to a feeling of "fullness". That feeling is a somatic feeling.
The nerve signal to your brain, saying you have enough calories for energy now, can arrive to your brain some 15-20 minutes after you begin to eat, even if you've consumed more than enough calories to get through.
Eating slowly gives your brain time to catch up to your gut, and hence when you arrive at your caloric needs, your brain can tell you that you have had enough. This feeling of "fullness" is nervous system fullness, not the somatic "fullness" people think about when they think of feeling "full".
Drinking water doesn't help with calories per se, but it does give the person the "feeling" of being full (somatic), and can help slow eating down until the brain catches up. Same thing with eating slow, and putting your utensils down between bites.