Milk is a colloid. It consists of water in which there are present minerals that include calcium, vitamins, fat and lactose. There are two types of proteins present in milk, around 80% of the protein is casein and the rest is called whey protein.
In its natural form milk is negatively charged. The negatively charged casein is dispersed as small micelles in the colloid. Vinegar is an acid that has a positive hydrogen ion and a negative acetate ion. When an acid is added to milk, the positive ions in it neutralize the negative casein micelles. These are no longer able to stay dispersed and coagulate to form a solid.
When vinegar is added to milk there is no chemical reaction between the acid and lactose. The precipitate that is formed when the two are mixed is denatured casein protein.