What does this means Joy is to sorrow as hope is to despair?

The "set up" of the sentence is a short way of comparing the first 2 feelings to each other and then comparing them with 2 other feelings.

You know that "joy" means happiness;and the opposite is "sorrow" which means sadness). Those two are at the opposite ends of our emotions or feelings (or "states of being").

You know that "hope" means holding on (to a wish for things to turn out well); and the opposite is "despair" which means giving up (on thought that things will turn out well.) These two are also at the opposite ends of emotions or feelings or thoughts or "states of being".

So a long way to say it might be "Happiness is (the opposite) of Sadness - (just the same as) - "Holding on" (believing things will work out), is (the opposite) of "Giving up" (thinking there's just no use).