In cooking meat like chicken, I've noticed that recipes say to close the lid and wait for few minutes. I'm trying to figure what exactly the effect created by this is. Any insight will be appreciated.
Hot air rises, and cool air sinks. This means that a lot of the heat that comes off the cooking surface goes right up in to the surrounding area instead of into the food you're cooking. It also carries off any hot water (steam) that gets caught up in it, which is often removed from the food you're cooking.
This means that meats turn out drier by the time they reach desired temperatures, rice might not absorb enough water and come out crunchy in the middle, some mostly-liquid dishes will lose too much water and turn out thicker than desired, the bottom will be burnt before the top side while the top side is still liquid, and so on.
As a super-simple and fun example, put an egg in a pan without breaking the yolk (use oil or butter if you don't have a non-stick surface). Cook it with the lid off. You'll get a "sunny side up" egg. Now do it with the lid on. You'll get a "basted" egg. Literally no difference except you have a lid in one case. P.S. "basted" includes several different techniques, I'm just mentioning one I've tried by accident, it turned out delicious.
Generally speaking, lid off or lid on is definitely part of the recipe to get the desired juiciness, cooking time, texture, or other attribute that you won't get if you do it the "wrong" way.
You might experiment with a few different type of foods with lid off and lid on, if you can spare it, to get an idea of how different foods react to the difference in temperature, water retention, etc. Be aware that some foods, like pasta, may rapidly boil over if you do this, as starch from the pasta will cause bubbles to form and seep out the top. Other dishes don't like lids as well.
This is basically part of the principle of a how a pressure cooker works. The pressure cooker builds up steam pressure, which cooks the food differently by increasing moisture retention, heat, and pressure. Using a normal lid on a pot or skillet won't get nearly as much pressure, but the heat and water retention will change how most foods cook.
In the specific example where a lid is added near the end, it's so that you don't lose too much moisture during cooking. Some recipes want the lid on immediately upon boiling, others half-way through, or in the last few minutes. It's all part of the technique to get the perfect cooked state without losing or retaining too much liquid either on the cooking surface or in the food.
In addition to keeping more heat in the pan by holding in more hot air and moisture, if the underside of your lid is reflective, for example because it's made of stainless steel, it will reflect some of the energy radiating from the pan back down into the pan and the food. The underside of Le Creuset's enameled cast iron lids is painted light beige and has the same effect (probably much less than a shiny steel lid).