Fibers are a way of deferring the main processing burden from interrupt ISRs to Fibers. Fibers are executed by the "RTOS Kernel", which run in an Interrupt ISR at the lowest priority. They are above the priority of all tasks, and normal code execution, but below the priority of all other interrupts (line user interrupt for example).
The main use for fibers are to take the load of IRSs, ensuring they can be short and fast. An ISR will typically save the condition it was interrupted on, instruct a Fiber to run, and exit. On exit, if there are no other interrupts pending, the code will execute the Fiber. Code execution will NOT continue at the position it was interrupt, but only after the Fiber has finished and exited. This way, the higher priority interrupts are not blocked, and we have transferred the "not so important" part of the interrupt processing from the interrupt ISR to the Fiber.