An expression for when you are trying to do/explain something which seems like it will never get done/be understood. Trying to enlighten people (your feeling of what enlightenment is) who do not want enlightenment is banging your head against a wall. Trying to make a perpetual motion machine, see why strapping buttered toast to a cat's back will not produce infinite power model, is banging your head against a wall. Trying to get your partner to understand what he/she has refused to understand for a long time is banging your head against a wall. The reason the term is used is because banging your head a against a wall does nothing but hurt your head. As well I think the word wall is used because walls are barriers.