Because when you’re sitting upright in a chair after a meal - which is the usual alternative to taking a walk - your stomach is compressed. When you’re standing up, your expanded, food-filled stomach and intestines can work better. If you just stand around instead of moving, however, that’s bad for your legs and back. So you start walking - not power-walking or jogging, that’s heavy work, but slowly ambling. (Remember, the human body is not designed* to be in any position, whether sitting, standing or lying, for a long time, you need to move and change your position).
Second, digesting is hard work. Blood rushes down to help with it and carry off the nutrients - that’s why you feel drowsy and can’T do a lot of heavy thinking after a full meal. The different gall bladders (don’t know English terms exactly) produces their different juices to digest the proteins, fat and sugars by breaking them down into little parts that can be absorbed through the intestine wall into the blood, while your stomach produces acid to kill off bacteria and keep proper pH for the enzymes to work. Plus all the other stuff besides the big three groups that are in the food - vitamins, rare minerals, preservatives, chemicals, …
Taking a slow walk (again, nothing strenous) helps keeping your circulation around, making it easier for the process than just sitting down, so all the blood flows down there, and has trouble coming back and going round.
Third, your intestines (not the stomach) definitly need movement and fibers in your food to prevent colon cancer, as numerous medical studies have shown. What better time than after a meal** to move that fiber stuff through your colon?
Also, if you over-indulged a bit, walking burns a few calories, and so eases your conscience better than sitting around. (The effect of burning more calories that comes with increased circulation can last up to 2 hrs after you stopped walking, so even 30 min. is better than nothing. Note that I’m not claiming that 30 min. slow walk will burn off a huge steak with sauce plus a cream cake.)
The only other good-for-your-body alternative is a siesta, where yo lie flat on your back, resting, so the body can concentrate on the digesting itself. You don’t battle with the natural drowsiness, or the low point in body rhythm between 12 and 4 pm, you accept it, ride it out and feel fresher after a lie-down or nap. (Just don’t overdo it).
As for late-night snacks: while medical studies have apparently shown that you don’t put on more fat from calories eaten before bed, still many people have bad dreams from sleeping with a full stomach, or can’t go to sleep when the body is busy digesting (a nap is different from night sleep). And the danger of stomach-burn is not good - you can get cancer in the throat from all that acid. The standard advice for treating stomach-burn is: stop eating late, and sleep with an elevated pillow (and avoid stress, best by using bio-feedback methods or similar).
- Yes, I know nature evolved and was not designed; I mean as a shorthand for “the forces of natural selection formed this body over time”
** Yes I know that the full digestion cycle can take up to 24 hrs, because food hangs around in the stomach itself for 2-4 hrs alone, then the small and large intestine. Still, at least you’re thinking of it now.