Milk is about 87% water. To make cheese it is necessary to separate the solids from the liquid.
Rennet is an enzyme which traditionally comes from the stomach of a young milk-fed calf, lamb or goat. It is what their digestive systems use to separate the fats, protein and vitamins they need from the water.
It causes the protein components in milk to form into curd and allows the liquid components to separate and run off as whey.
Most rennet today, however, is made by cloning vegetable versions of rennet. Animal rennet will vary a lot in its strength. A cloned version will give a standard strength, thereby giving greater consistency to the process.
It also makes the cheese suitable for vegetarians.
Some makers believe that animal rennet is better for well-aged cheese. Parmesan, which can easily be eight or more years old, must be made with animal rennet if it is to qualify for the name.
Ask your local restaurant however, and most will have no idea as they sprinkle it over your vegetarian pasta bake.