Non-biodegradable waste will NOT break down (or won't for many many years). Examples are plastics, metal and glass. Some dangerous chemicals and toxins are also non-biodegradable, as are plastic grocery bags, Styrofoam (polystyrene), and other similar materials but will eventually break down over time.
BIOEGRADABLE: The waste which break easily by the action of some micro-organism (i.e. bacteria) an also break in non-poison form.