Hey :wave:,
Traditionally a Shakespearean play needed to appeal to a wide audience, due to its context and the role of theatre. A fool or clown in a play was meant to appeal to less educated theatre-goers - some other aspects which might have appealed to them include slapstick comedy, fight scenes with swords etc. However, the fool doesn't always serve such a mundane purpose, as santaslayer said.
Maybe if you have to analyse the role of the fool, you could do it traditionally and then psychoanalytically so you have at least two ways of looking at that character. Use examples and analyse them to support both.