White balance tells your camera the color temperature of the environment you're shooting in. Different types of light have different colors. For example, incandescent bulbs (like what many people put in a lamp) have a very warm color. The fluorescent lights (if you're reading this in an office, look up) are a little bit cooler. Daylight is cooler yet. Before you begin shooting, you have to adjust your camera's white balance according to your setup.
Professional cameras, like DSLRs, give you fine control over the manual settings of shooting video and allow you to achieve the shallow depth of field (background out of focus) that people rave about. While they're primarily used for photography, DSLRs are incredibly small, work great in low light situations, and pair with a wide range of lenses — making them perfect for video. However, DSLRs do require some training (and additional purchases) of lenses.