Non-renewable sources of energy are those sources that take millions of years to form and thus are limited in quantity and cannot be regenerated in the near future. Examples of such sources are coal, petroleum, natural gas, etc. In comparison, renewable energy sources (such as wind energy, solar power, etc.) are renewed very quickly and hence are practically infinite in quantity.
In spite of the environmental and economic issues of non-renewable energy sources and the recent surge of interest in renewable sources, non-renewable sources are still very relevant. Most of our energy requirements, whether for electricity, heat or transportation are still fulfilled by non-renewable energy sources. Most of our grid and infrastructure is built for non-renewable energy sources and modification of this infrastructure is resource and time intensive. Non-renewable energy sources are still more efficient than renewable energy sources and are more reliable, too (for example, we cannot harvest solar energy during night or dark weather, etc.). Non-renewable energy is also spread throughout the world in one form or another, and is not as location dependent as renewable energy sources. For example, we can transport natural gas to areas where it is not found, however, we cannot easily do the same with solar energy or wind power, etc.
Hence, non-renewable sources of energy are still very important.
Hope this helps.