The idea of having a program understand "english" (or some other language which humans speak). While this sounds like a really simple goal, it quickly gets very complicated. English is very ambigious, and computers are very exact, which tends to lead to some really interesting problems.

the pig pen

does this mean the place where pigs live? or the writing implement that looks like a pig?

time flies like an arrow

Apparently this has 5 different possible meanings some of them are:

time flies, nasty creatures like fruit flies, like to eat arrows.

time flies, really fast, like an arrow

Fruit flies like an orange. -- CraigBox