If you usually drink your coffee with lots of cream and sugar in it, you might be surprised at how bitter plain black coffee can taste. Bitter means "having a sharp or harsh flavor."
Bitter describes a particular pungent taste, like the sharpness of very dark chocolate (which is sometimes called bittersweet for its mixture of the two flavors). If you imagine taking that bitter taste on your tongue and turning it into an emotion, you've got another meaning of bitter: a resentful, angry feeling. And if you turn that bitter flavor into a physical feeling, you've got an adjective that describes a sharp, unpleasant sensation, like a cold, bitter wind.