means The quality of being sharp and acidic in taste, or by extension, the bracing sourness of a sharp-tongued remark.

from From "tart," meaning sharp to the taste, which traces back to Old English "teart" — sharp, severe, painful. The food sense (the pastry kind of tart) is a completely separate word borrowed from Old French; these two tarts only look like siblings by accident. The "-ness" is the workhorse English suffix that turns a quality into a noun, the same one quietly doing duty in "sweetness" and "sharpness."