It's beef stock that has been boiled and reduced until it becomes like a syrup or paste. It's highly concentrated beef flavor so if you use it start with a small amount and only add more as you taste.
In Japanese, "Demi" does not have a specific meaning as it is not a native Japanese word. However, it can be interpreted as a loanword or used in context, such as in the names of food items like "demiglace" (デミグラス), which refers to a rich brown sauce. Additionally, "Demi" might also be associated with the French prefix meaning "half," but this usage is not common in Japanese.
Well, white sauces are by their very definition milk or milk product based sauces, rather than broth, stock, or say tomato based sauces. Brown gravy or au jus are by definition based on beef broth, beef stock or beef demiglace, whereas country gravy is a milk based gravy, generally served with pork chops or chicken fried steak. If you're asking why milk versus half and half versus light or heavy cream, my guess is the recipe you are looking at wants less fat than half and half or cream provide.