It's easy to follow the directions on the recipe, but what's going on? The science of food is where the magic happens. There are many great references (one of my favorites if you want to get to the fundamentals of what is going on is Food Science from Guelph University), on the complex nature and reactions of milk and dairy products but here are some key points:
Start with the milk. Using cow's milk as an example. It a blend of 3.3% proteins, 4.6% sugars and 3.9% fat in water with various minerals - so about 12% - 13% solids.
Of special interest for the moment is that the sugars are mostly Lactose and the Protein mostly Casein.
The short story is this. Various bacteria will eat Lactose sugar and produce Lactic Acid. The Lactic Acid reduces the pH of the milk and once it starts getting acidic the Casein denatures - think of denaturing as a ball of string unwinding. When it does this you get a gell - called "curds" and it separates from the "whey" (as in Little Miss Muffet). Now you have two parts. The "whey" has most of the water, the remaining Lactose and the Lactic Acid and some proteins that require even lower pH before they unwind, and the "curds", a solid mass of nutritious fat and protein and some water, sugars and acid.
The art of making cheese, yogurt and a whole world of other products is how this process is manipulated and fine tuned. How quickly this all happens, how completely, how much sugar is left and how much acid, how it is aged.... Just like wine, cheese is a natural product and once we start the ball rolling with bacteria they will eat what they can until you stop them or they run out of stuff to eat or die. Each will produce specific byproducts that will have taste and smell and texture.
The art is in how this is managed - one path leads to Yogurt the other to Camembert....but it all started with milk.