If you're apprehensive, you're anxious or fearful. If you just got run over by a crazy bicyclist, you might be a bit apprehensive crossing the street.
Apprehensive is from a Latin word meaning "to seize," and it originally meant "quick to seize impressions or ideas, perceptive, intelligent." Now it means "anticipating something bad, fearful of what may happen." Synonyms are afraid, which suggest a more immediate fear, and fearful, which suggests a more general temperament ("a fearful child"). You can be apprehensive about a situation while being an optimistic and courageous person in general.