The central governor is a theoretical idea that tries to explain an alternate mechanism for fatigue in exercise. According to this theory, people's muscles aren't actually depleted when they start to feel tired. Instead, the theory suggests that a mechanism called the central governor creates a feeling of fatigue in the body as a way to protect a small energy reserve for emergencies. So, the person feels tired and stops exercising before actually running out of steam in a physical sense. The central governor concept is still very much debated, and many fitness experts don't agree with it at all.
The traditional theories of exercise fatigue are much more focused on physical aspects of muscle function. For example, muscle fibers tear during strength exercise, and the body burns carbohydrates and fat when people engage in physical exertion. Most fitness experts agree that these things act as limits. They believe that the muscles literally become depleted of energy reserves, which directly leads to pain and discomfort. Those who agree with the central governor idea don't necessarily dismiss the basic concepts of physical energy, but they don't think physical limits are primarily responsible for most fatigue.
Central governor proponents point to many things that happen at sporting events as evidence for their theory. For example, there are studies that show runners who are absolutely exhausted are able to run faster at the very end of their races. There are similar occurrences in other sports where athletes are sometimes able to find an extra burst of energy in the most important situations, regardless of how tired they might feel. For example, a boxer may rally near the end of a fight and find the energy to knock his opponent out even though he was almost too exhausted to move in the previous round.
There are also some laboratory studies that support the central governor idea. Scientists have done research designed to trick the mind into thinking it was receiving sustenance when it actually wasn't by having people taste sweetened drinks without actually swallowing them. Those studies have shown those tasting the drinks can perform for longer even though they didn't actually get significant levels of carbohydrate energy. There are also studies showing that mental fatigue can directly lead to physical fatigue. These studies and others like them seem to show a more direct connection between mental function and fatigue levels than many other traditional fitness experts would have expected.