I need help understanding the difference between real and protected mode. If someone could explain it to me or point me in the direction of a book that will, ir would be very much appreciated.

Many programs are still written in real mode.
Dos programs are usually real mode, it means that they use only up to 1024K mem, no more.
These are just programs with few intructions, with a few more added, it can change over to protected mode and use as much mem as it wants. But once the chip (286 and up) are running in protected mode, it cant run real mode programs.

To understand the difference, you should have a look to the x86 processor familly.

You will the discover that it uses a segmented memory sheme. That means that when you access memory, the processor will use a Segment value and an Offset, and will do a 'specific calculation' witgh those two values to build the Final adress.

Real and Protected mode are Processor working mode (only for CPU >= 80286)

Il real mode, the Segment is really a hardware base adress.
In protected mode (which can have differents flavours) the segment is in fact a SELECTOR: reference to an entry in a table describing a memory zone. As each selector can adreess 64Kb in mode 16 (and much more in 32) that allows larger memory acces.
Protected mode means that the processor will catch any invalid Selector load or access.

Memory communication between protected mode and non protected mode (DOS) makes it necessary to Translate the memory calls and addres. Some product help you (Pharlap, PowerPack....) by giving you a loader (which starts in real mode and than starts you progralm in protected mode)and some support to accees usual DOS finctions.

See DPMI 0.9 description .