Deep-frying is not unlike baking, with the hot air replaced by hot oil. The physical principles that operate are much the same. Just as the aim is to dehydrate and brown the surface of a loaf of bread in the oven, so it is with browning deep-fried food.
When food is placed in hot oil, the first thing that happens is that water on, or just under, the surface of the food boils. The steam bubbles away, creating a buffer zone between the food and the oil. The food is actually cooking by steaming – cooking in oil is a humid cooking style. Food does not become oily while it is cooking in the oil, since the food is not much in contact with oil.
While it’s still steaming, the surface of the food cannot brown because its temperature is maintained at ~100C until the water boils away and the surface dries. Browning will only start when surface temperature can exceed ~130C.
You can actually tell when browning is going to start by listening. When most water has been evaporated off and the steam diminishes, the oil will become noticeably quieter. Then everything happens quite rapidly, and the food will heat (above 100C), crisp and brown quickly. The challenge is to ensure that heat (by conduction) has penetrated the food sufficiently to cook it by the time the surface layers have dehydrated and started to brown. Hence food is either pre-cooked, or cut in to small-sized pieces.
One way to slow the crisping process and allow time for the food to cook through is to batter it. This helps with larger pieces of food such as a fish fillet. The batter is moist, and it forms a shield around the food so steam is trapped between batter and food and the food is given a longer chance to cook in the humid environment.
The first batters were designed precisely for this purpose – a flour-water paste to encase the food and help cook it through. They were not meant to be eaten.
Then someone worked out that they could have it both ways – a batter that serves its purpose, and that is edible too! In fact, often the batter is the point of it all.