Imagine a power plant feeding a utility in a small town with a single transmission line to the larger utility system. Imagine a fault on the transmission line that opens its breakers leaving the power plant just feeding the small town. That generator is islanded on that town.
The problem is the generator does not know it has been islanded and assumes it is still feeding power into a large grid. The unbalance between generation and load will either cause frequency to increase (generation > connected load) or decrease. Protective relaying and turbine controls can either respond to the frequency change and try to keep the generator islanded or trip the unit, sending the town and the power plant black. Another problem occurs if the transmission line breakers do not have a means of resynchronizing the island with the main system. (Example drawn from a true event in Northern California, USA).
The power plant engineers challenge is to decide if the plant can be islanded (many can't) then decide how islanding is going to be detected, controlled and how the system will be returned to normal. When a plant goes to island mode, the governor must immediately switch from load (MW) control to frequency control (isochronous control or constant speed control).
From a protective relaying perspective, utilities usually require under/over frequency and voltage relaying at the power plant tie point to detect islanding and dump the generator off the system. The relays detect the generation-load mismatch by seeing the sudden frequency or voltage variations. In the above example, the town's load just happened to match the generator output (12 MW) so the generator operated islanded on the town for a few hours. No one knew until the boiler fan VFD's tripped due to the frequency drift. The operator dumped the generator breaker and was surprised to see all the lights in the plant and town go out.