After heating and pasteurizing the milk, which is simply killing whatever is currently living in it, the first step in the cheese making process is to separate the curds which will make up the cheese, from the whey.
To understand what is going on here, we need to understand what is in milk, i.e. what is milk made up of? The important parts of milk, or rather, the parts of it that are of primary concern in making cheese, are water, fat and lactose. Lactose, we'll come to later. For now we need to concentrate on the water and the fat.
Water and fat don't mix. At the level of molecules, water is polar. Which is to say that the charge is spread unevenly over the molecule with one end tending to be positive and the other negative, due to the possible arrangement of atoms with respect to other and the relative strength of the atoms charges.
The end result is that water, being polar, can arrange itself in a comparatively orderly manner with other polar molecules such as water or sugar. That order is disturbed however by non-polar molecules such as fats, which have the charges of the constituent atoms, relatively well spread. The two types of molecule are called, respectively, hydrophilic and hydrophobic.
These molecules naturally clump together into small structures called micelles, small roughly spherical bodies with their hydrophilic portions facing outwards and their hydrophobic portions facing inwards. These small bodies form an ideal place for hydrophobic fat molecules to hide from the water molecules. In addition, all hydrophilic parts of casein are all negatively charged, which keeps the micelles away from each other.