The ear of a sow (a female pig) is notoriously rough and bristly, whereas a silk purse is just as obviously smooth, elegant and luxurious. Clearly, you cannot make one out of the other. What it means is that certain things/people are quite unsuitable for certain purposes. For example, a schoolboy who cannot pass GCSE subjects might ask the Careers Master what his chances of becoming a brain surgeon are. The teacher might - rather unkindly - say, "You can't make a silk purse out of a sow's ear, Smithers!"