The turn coordinator, attitude indicator (artificial horizon) and heading indicator are based on gyroscopes. Gyroscopes have spinning wheels that maintain their position as their anchoring hardware moves around them. These wheels require some sort of power to spin; the turn coordinator is typically electric, while the other two are vacuum powered. I don't think I ever wondered "why vacuum?" before, but you can probably guess that I did today!
There's either a vacuum force created by design of the system, or a vacuum pump within the system, for these instruments. It sucks air from the intake, through a filter, through tubes and instruments, through a pressure release valve, and then exhausts it. The book doesn't have a diagram, but I'm imagining fins on the gyro wheel to catch the air, like on a water wheel for catching water. As long as the air is flowing, the wheels will be spinning.
Because of precession, or the introduction of error in gyro-based readings due to friction, gyro instruments must be periodically cross-checked and/or recalibrated. Most notorious is the heading indicator, also called the directional gyro or DG, which should be compared to the whiskey compass (magnetic) every 15 minutes or so. The whiskey compass, however, gives temporarily inaccurate readings while turning, accelerating or decelerating and is affected by turbulence as well.
Another direction-relevant complication is variance, or the difference between true north and magnetic north. Instruments are set relative to a magnetic reading, yet charts and publications use a true north reference. Since the magnetic field of the Earth changes from place to place, it's important to know the variance at your location. To give you an idea, the variance along the east coast ranges from roughly 0 degrees west to around 20!
