Sustainable Energy Supply – Energy that can potentially be used well in to the future (continue forever) without harming future generations

NOTE: Sustainable energy is the combination of energy savings, energy efficiency measures and technologies, as well as the renewable energy sources.

To understand the words "sustainable energy source" you need to remember the meaning of sustainable and then energy supply.

Sustainable – able to be maintained or continued

Suds couldn't remove the stain; I wasn't able (sustainable) to get the stain out. It continued to annoy me.

Energy supply – in this context includes solar, wind, hydroelectric, geothermal and biomass

So, a sustainable energy source is energy that can be maintained or continued.

The difference between renewable and sustainable is as follows: 
If I have a single tree in my backyard and I cut it down: this is a renewable source because the tree will grow back from the stump, but very slowly. If I try to heat my house with the tree this is not sustainable because the renewable rate is too slow.

A sustainable energy supply is therefore one that can continue forever without harming future generations.

This deforestation of tropical rain forests is NOT sustainable.