Non-renewable resources, such as groundwater or fossil fuels, are resources used at a rate higher than the rate at which they can be replenished within a human time frame. Coal, for example, is only created under certain conditions, and it takes millions of years to achieve a form that is useful for energy generation.
Oil is similar to coal in that it is formed by deposits of organic matter, held in anaerobic, or oxygen-free, conditions, for very long periods of time. Oil deposits are either not being laid down in the modern age, or they are being laid down at such a slow rate that human consumption far outstrips the environment's ability to replenish the supply.
Other non-renewable resources recharge on a shorter timescale than oil or coal, but they are still regarded as non-renewable because human consumption is high enough to impose a net drain despite the faster recharge. Underground aquifers fall into this category, as human habitation typically extracts water from natural sources faster than rain and runoff can fill it back up.
Wind and solar power, as well as timber managed in a sustainable manner, are regarded as renewable resources. This is in part due to their high recharge rates and low levels of exploitation.