"What is a Kernel? The Kernel is the Foundation in which everything else builds upon in any software system.
[Car Analogy]: Kernel is like the Engine, Electrical system and the Transmission to a car. The Library, Framework and the Apps [AKA ROM] are the body frame and the rest of the Car." - faux123

Think of a computer as a company. You have corporate at the top, management in the middle, and employees at the bottom.

Corporate is the shell. They call the shots, while not necessarily knowing the specifics of what goes on at the lower levels. They ask for something and it gets done. Any input they receive must come from management.

Management is the kernel. It knows how to take orders from corporate, and allocate employees to get the job done. It knows all the employees by name, their abilities, and how to handle them. It also takes input from employees and passes them along to corporate when appropriate.

Employees are the hardware. They get their orders from management then get the job done. All communications with the outside are handled by employees, whether it's taking input or displaying the finished results.

An example: You drag the notification shade down. Employees detect your touch input and report the coordinates to management. Management translates this into a touch event that corporate can understand. Corporate receives this report and tells management it needs to draw the notification shade at the location of the touch event. Management breaks these instructions down and allocates employees to create the shade - fetch the required resources from memory, calculate the inertia and location of the finger at every frame, find where the shade should be drawn, then get the graphics to draw the shade.