means The quality of being unclear, imprecise, or not definitely or explicitly stated.

from From Latin 'vagus,' meaning 'wandering, roaming, rambling' — the same restless root that gives us 'vagrant' and 'vagabond.' A vague statement, then, is one that won't settle down in one place; it drifts. English picked up 'vague' through French in the 16th century, and tacked on '-ness' to name the wandering itself.