For a dual mode processor, some register has a bit that determines the current mode of the processor.

We'll refer to these two modes generically as user mode and kernel mode.

If the processor is in kernel mode, then all machine instructions for the processor can be executed.

In user mode, some of the instructions will "trap" and not execute. These are called privileged instructions.

The term kernel will refer to the operating system code or at least to the part that does the work that requires extra privilige.

The mode of the processor should be user when user code is executing and kernel mode when kernel code is executing.