The afternoon might be metaphorically stretching, that is getting longer and longer in the persons mind. It might seem like a sunny afternoon stretches if you are going to spend a lazy afternoon on the beach reading a book. It is a poetical way of describing this sensation. The afternoon might also stretch for a bored child, seeming to get longer and longer because they anticipate they will be so bored. Maybe their friends are on holiday and they are all alone.

Actually, it should mean "the afternoon was just starting and he had the whole afternoon to do something, or to wait for it to end, until evening comes". Stretch out here refers to the length, the duration of the afternoon. A long afternoon may be positive or negative, depending on whether you're waiting for something painful to end, or enjoying your day off :o)

This is english. In no language you should ask WHY as the natives decide the rules and the usage of course. Anyways, afternoon stretched means afternoon passed and evening came. hope it helps :)