Shallow frying is where you put a little bit of cooking oil into a saucepan or skillet and then fry the foods in the shallow oil.
You put just enough cooking oil in the pan to cook the foods in the oil and don't completely submerge the food like you would when deep frying.
For example you could put some cooking oil into a pan and then put some potatoes that are sliced up into the pan and that would be shallow frying.
Shallow Frying is typically used to prepare portion-sized cuts of meat and fish, and patties such as fritters etc whereas deep frying is mostly used for french fries, chicken and other meats.