What‘s the rationale for homemade yogurt? Is a yogurt machine necessary?

Yogurt forms when bacteria ferment the milk sugar, known as lactose, into lactic acid. The lactic acid makes the milk more acidic (lower pH) causing the proteins to coagulate. Figure 1. The nutrition facts for whole milk yogurt. The acidity of yogurt tends to be in the range of pH 4.The more lactic acid produced, the tangier the yogurt will taste. The final taste and consistency of the yogurt can be influenced by the type of yogurt starter used and length of incubation time. The thickness of the yogurt results from the coagulated proteins determined by the fat content of the milk, the yogurt starter, and amount of milk solids (protein). Adding nonfat milk powder (milk solids) to cold milk before heating will result in a firmer yogurt. However, adding nonfat milk powder to heated milk will cause some proteins to coagulate and form strings. The yogurt starter is the source of bacteria. The tartness of the yogurt will depend on the bacteria culture that is used, as well as how long the yogurt has fermented. A yogurt starter can be a store-bought yogurt that has active live bacteria, or a previously made batch of yogurt that is about 5 to 7 days old (for the freshest and most active bacteria). Freeze-dried starter or an heirloom culture bacteria in powder form can often be purchased at local natural-food stores or from online vendors. 

Reference:

https://extension.oregonstate.edu/sites/default/files/documents/8836/fs173emakingyogurt.pdf