In simple terms, x86 protected mode and real mode refer to two different operating modes of the x86 architecture in a computer.

Real mode is an older mode that was used in the original IBM PC and in early versions of the x86 architecture. It provides limited memory access (1 MB) and limited security, but is faster and simpler.

Protected mode, on the other hand, is a more advanced mode that provides a more secure and efficient environment for running modern operating systems. It offers access to a much larger memory space (4 GB or more), hardware protection, and virtual memory, but is slower and more complex than real mode.

Most modern operating systems, such as Windows and Linux, run in protected mode, while real mode is mainly used for backward compatibility or for running certain low-level system software.
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