Rennet makes the milk thick. This is because rennet contains enzymes. An enzyme is a kind of scissor that can cut parts of a protein and therefore also from the most important protein in the milk: the cheese dust (= casein).
The cheese dust particles form small balls of protein molecules and lime salts. There are many protrusions on the outside of these balls, say hairs. Normally, when the particles collide, the particles do not touch because the protrusions maintain the appropriate distance and the particles remain neatly distributed in the milk. When an enzyme is added to the milk, the hair is cut off and “bald spots” appear on the cheese dust particles. The particles can now touch and stick together and a network of protein particles is created. This will make the milk thick.
Milk with a low protein content forms a less dense network. The milk curdles less firmly. Sheep’s milk, for example, has a higher protein content, which makes it curd more firmly. A high fat content makes the protein network less solid, because the fat globules disrupt the cohesion.