If you've been working with computers since the days of DOS, the difference between real mode and protected mode is easy to understand. But if your computer life began after Windows took over, the difference might not be as clear, and you might not appreciate the importance of the distinction.
If your computer is in real mode, software communicates directly with the computer's ports and devices. For example, when you print a document, the software sends the data stream directly to the port that holds the printer. However, this paradigm doesn't work in a multitasking OS. Imagine what would happen if multiple programs sent data streams to the ports simultaneously. Ports are dumb, and they have no ability to filter or arrange data streams to match the sending programs.
If your computer is in protected mode, the system's ports and devices are protected from the applications that use them. The software thinks it's sending data to a port, but it's a virtual port. The OS is grabbing the data stream and managing it, to ensure that all applications have equal access and to ensure that data from each application is appropriately preserved.