When you acquaint yourself with something, you familiarize yourself with it. When you visit a new city, you should acquaint yourself with the layout of the streets so you don’t get lost.
You can also acquaint yourself with another person, by introducing yourself and getting know them. When you see the moving truck pull in across the street, you might want to run over and acquaint yourself with your new neighbors. The word acquaint comes via French from the Latin accognoscere, which is made up of ad- “to,” or “toward,” and cognoscere “come to know.”