If you're unacquainted with someone, the two of you have never met. If you and your next-door neighbor are unacquainted, it would be friendly to introduce yourself.
When people are unacquainted, they don't know each other, and if you're unacquainted with something, it's completely unfamiliar to you. So if your best friend is unacquainted with the music of your favorite band, you might decide to buy her a concert ticket, so she can become familiar (or acquainted) with their music. The Latin root, accognoscere, means "know well."