A base coat of paint is typically the first layer of paint put onto an object, sometimes intended for the application of the color. Base coats also tend to operate as the base of the color scheme, where other layers of more transparent or colored paints can be then coated on smoothly.
In the context of applying a paint job to a car, the base coat is where all the color from the new paint job comes from. They are likely urethane-based paints that need to be mixed with an activator which allows the base to catalyze and form an adhesive shell to the surface once it is applied. Activators, themselves, can be of a fast, medium or slow variety, intended to categorize the speed of their reactions to achieve this purpose. Base coats can come in other chemical variations, as well.
Within the context of home improvement projects, like painting walls and such, a base coat has a similar function. When someone applies a base coat to their wall, the paint is meant to provide a clear, flat surface that will operate as the base for the applied color. In this way, any little dents or scratches in the wall can be covered up and the walls can be recolored with a clean, new color to be layered on once the base coat dries.