It basically means the taste of vinegar(醋 or 酸醋) or unripe fruits like apples and oranges. And it means "to be jealous" if we say someone is 酸. Specially, if someone is jealous of a rival in love, we say he/she 吃醋("eats vinegar" literally, though we usually drinks it). Besides, we can name the one who often "eats vinegar" a 醋坛子(vinegar pot).
When someone is sad, miserable or sorrowful, we can also use 酸. For example, 心酸, 心 is heart. 心酸 means "to feel sad".
And it can mean "acid" in chemistry. Sometimes it refers to "gastric juice". It means "pedantic" sometimes. For example, 穷酸秀才(poor and pedantic xiucai). This is a despising address to the scholars. 秀才(xiucai) is one who passed the imperial examination at the county level in the Ming and Qing dynasties. Now it usually means scholars.