Pan frying is frying in a pan. Typically it implies that a frying pan is used with an amount of oil. Pan frying would be used for something like thin white fish or trout. It's also used for browning chicken, Quorn meat, and tofu.
When pan frying, the amount of oil in the frying pan is adjusted to come part way up the side of the food being fried. Generally, the bottom 1/3 to 1/2 of the food will be in the oil. The amount of oil is between that used in deep frying, where the food in completely immersed in oil, and sautéing, where only the bottom surface of the food is in contact with the oil.