All three of these examples try to maximize the ratio of surface area to volume to try to facilitate some type of exchange.
In the case of a leaf, it has a very small mass (and volume) but a large surface area to help maximize the amount sunlight that it can capture. The more effectively the plant can capture sunlight with a relatively small number of leaves, the more food it can produce via photosynthesis.
In the case of a car radiator, the surface area is maximized in relation to the volume of water/coolant. In this way, more of the water is near the surface of the radiator which will allow it to release its heat and cool faster. The faster the radiator can cool down the coolant, the more effectively the engine will function.
In the case of alveoli, the surface area is maximized to help facilitate gas exchange. The alveoli in the lungs absorb oxygen from the air and release carbon dioxide from the body into the air. The more surface area there is in the alveoli, the faster and more efficiently the gas exchange happens. This is important so that the body can endure during physical exertion without getting to winded too quickly.