Vagueness is a state of being unclear or uncertain. The vagueness of your directions won't be very helpful to the lost pedestrian who's trying to find the closest subway station.
If your parents ask what time you went to bed, you might say “nine-ish” and hope they don’t question your vagueness. Vagueness can also be visual, like the vagueness of shapes in the fog. The Latin root of vagueness, vagus literally means "wandering" and figuratively means "vacillating or uncertain."