While there are tons of foods that can taste good or even better the next day (pizza), many foods suffer from short term storage. Meat is particularly susceptible and can obtain flavours which some characterize as stale, metallic, or cardboard-like. In academic literature and industry, this is called warmed-over flavour (WOF).
A fundamental concept to keep in mind is that food is dynamic in its physical and chemical composition, even after cooking. Over time, the chemical make up of a stored food will be different than when it was first cooked.
In a nutshell, the chemical changes that occur during food storage are responsible for the staleness in leftovers. There is also water loss, but I'll focus on the chemistry side. Food scientists point to lipid oxidation as the main factor for developing WOF. The typical victims of storaged induced oxidation are lipids found in the outer membrane of cells (phospholipids, sphingolipids, glycolipids). Fat tissues are mainly saturated fats, which are not as suspectible to oxidation.
Meats with more unsaturated fat content are more prone to developing WOF.
Fish (most likely) > Poultry > Pork > Beef > Lamb (least likely)
So why is meat more likely to develop off flavours compared to other foods?
Meat contains iron embedded proteins. Iron is released from these proteins (hemoglobin and myoglobin) during cooking. This free iron can then speed up (catalyze) lipid oxidation during storage, hence meat is particularly vulnerable to developing that "off" taste. I have created some diagrams to show how lame I can be and for illustration purposes (I guess).
So, how do we minimize these warmed-over flavours?
1. Antioxidants - when present, some of these molecules are oxidized instead of the membrane lipids. Antioxidants, in a sense, sacrifice themselves. Antioxidants are readily found in garlic and in herbs and spices such as basil, rosemary, sage, thyme, etc.
1. Citric Acid - when present, will bind (chelate) metal ions such as iron that contribute to oxidation. Citric acid is abundantly found in citrus fruits like lemons, limes, and oranges.
Methods 1 and 2 highlight a not so obvious benefit of marinades, dry rubs, and glazes. Pretty neat, huh?
3. Limit oxygen and light exposure - keep your fridge dark and remember to wrap and cover containers.
4. Use a gravy or sauce - this limits oxygen, masks bad flavours, and could contain Maillard reaction products which can also inhibit oxidation.
For the scientifically inclined:
Igene JO, Pearson AM, Dugan LR & Price JF (1980). Role of triglycerides and phospholipids on development of rancidity in model meat systems during frozen storage. Food Chemistry 5(4), 263-276.
Pearson AM & Gray JI (1983). Mechanism Responsible for Warmed-Over Flavor in Cooked Meat. In The Maillard Reaction in Foods and Nutrition. American Chemical Society.
Trout GR & Dale S (1990). Prevention of warmed-over flavor in cooked beef: effect of phosphate type, phosphate concentration, a lemon juice/phosphate blend, and beef extract. Journal of Agricultural and Food Chemistry 38(3), 665-669.