We know that some of the resources we rely on have the potential to run out, while others are renewed as soon as we use them. We've deemed those resources that seem to be infinite "renewable resources", while those that appear to be finite are called "non-renewable". The key difference between the two all comes down to speed.
Renewable resources definition
A renewable resource is defined as a resource that is replenished by the environment over a relatively short period of time. Basically, it is a resource that can be sustainably used by mankind ad infinitum. In some cases a resource appears to renew as soon as it is consumed, while in other cases the renewal can take decades. The key, however, is that a renewable resource is replaced by the environment within the span of a human generation.
Examples of renewable resources
There are dozens of examples of renewable resources in nature. Farm products, livestock, and fish are all considered renewable as long as these resources are harvested in a sustainable manner. What makes these renewable is the fact that all reproduce: livestock, for example, replace themselves with their young. Another example of a renewable resource is water. While water doesn't reproduce, it does run through a renewing cycle, evaporating to form rain clouds which then return water to the earth in the form of rain.
Five energy sources are considering renewable, including wind, solar, hydro, biomass, and geothermal. In the case of wind, solar, hydro, and geothermal, these resources renew almost on demand, as the sun comes up every day and the wind never stops blowing for long. Meanwhile, biomass is renewable because biomass like timber can be sustainably harvested, even if it takes decades for a tree to mature.
Non-renewable resources definition
Non-renewable resources, on the other hand, are not easily replenished by the environment. Many of these resources were originally formed with intense heat and pressure over a very long period of time. Because of the time it takes to form these resources, they're deemed non-renewable -- mankind has the potential to use up the entire resource base before it has enough time to renew. Further, in some cases the conditions needed to produce the resource are no longer in place.
Examples of non-renewable resources
Fossil fuels, including coal, natural gas, and oil are prime examples of non-renewable resources. Oil, for example, is derived from ancient fossilized organic materials such as algae that settled into the bottom of ancient seas and were buried under sediments. Further, the conditions to form oil required not only a lot of time, but the right temperature, as kerogen forms when the temperature is too low, while natural gas is the result of higher temperatures.
Other examples of non-renewable energy resources include nuclear fuel like uranium. While nuclear fuel is more sustainable and cleaner than oil or coal, uranium itself is only formed in supernovae. In fact, all elements with atomic weights higher than that of iron are only naturally formed in supernovae. Suffice it to say we shouldn't expect those conditions to return anytime soon.
Almost any resource is renewed by the environment given the right amount of heat, pressure, time, and inputs. However, for several key resources the conditions are no longer ripe for renewal. Because of that, these are non-renewable resources, meaning once they are gone they will not be replaced by nature in a meaningful time frame, if at all. That replacement speed is the key difference between renewable and non-renewable resources.