Why is food processed at all? In other words, what does processing (in various ways) help to prevent?

Food processing occurs on many levels from simple task under taken in our kitchen to chemist based food science. The main goal of processing regardless of the method is to lower the risk of food borne illness. Processing can eliminate the opportunity for bacterial growth, create products that require less energy to store, and improves the appearance of the food over its shelf life. Bacterial growth is on the leading cause of food born illness. Food science makes use of chemistry to create products that resist contamination over time and limit colony growth. Some processing is largely natural like the use of sorbic acid to prevent bacteria growth. Potassium Sorbate is a nature identical chemical that was discovered by the French in 1850 and is till used today to extend the shelf life or a product.
The most hazardous food products require temperature control that can be costly and energy intensive. In order to store food products over long periods of time they can be canned or pickled. Both process the food and maintain the nutrient value while eliminating bacteria and extending the shelf life.

There are many reasons that food is processed. Although some celebrities and public figures are radically opposed to all forms of food processing, most scientists and health experts take a more judicious approach, arguing that, while some forms of food processing are unhealthy, other forms are essential to protect consumer health.
The first types of food processing are those designed to help preserve food from spoiling. Long before the advent of modern technology, people would smoke, dry, salt, pickle, can, freeze, or jam foods to preserve them. For example, if a hunter killed a deer, the meat would spoil long before it could be completely consumed and so the family might dry, smoke, or salt much of the meat so it would not spoil. Modern chemical preservatives add to the repertory of methods of preservation.
Next, processing can be required to make certain forms of food safe or edible. Milk pasteurization kills potentially harmful bacteria, unlike homogenization which is done for purely aesthetic reasons. Many types of processing, including heating, are used to kill bacteria.
Less healthy forms of processing, such as the forms of processing which create white flour from whole wheat flour, remove essential nutrients for economic reasons. Processed cheese is far less expensive to produce than real cheese and has a longer shelf life. Some highly processed foods designed to be inexpensive to produce and shelf-stable are lacking in many essential nutrients and are often high in unhealthy ingredients such as salt and transfats (themselves a form of highly processed plant oil).
https://www.cdc.gov/foodsafety/production-chain.html