When you're acquainted with someone, it means you know each other. If you're taking the city bus and realize that you know several of your fellow riders, you could say, "I'm acquainted with half of the passengers on this bus."
As long as you know something or someone fairly well, you are acquainted with it, so you can be acquainted with a city, a mathematical idea, or a particular poem. The trickiest thing about the word acquainted is the way it's spelled. Like the words acquit and acquire, you just have to keep in mind that a c needs to go before the qu. After you've spelled it several times, you'll be well acquainted with the correct spelling.