I have written a lightweight RTOS/Multitasking system for the Pic 16-bit micros and posted it on EDA board here.
It includes documentation that describes how the system is implemented plus examples that you can run using mplab sim.
It uses the logic analyzer window so you can see when tasks are running.
I dont know if this will help you, but it details how basic RTOS/multitasking is implemented and includes full sourcecode.
The kernel is a central control thing. A bit like the central control room for an airport. The planes all fly by themselves but need the control room for good and safe operation.