It's a scale of measure to show how efficient (input power vs output power) a Power supply is. It's dependant on your input voltage (mains supply).
The basic 80Plus means that at 20,50 or 100% PSU load, the PSU is at least 80% efficiency, though this is only valid if you are using a ~115V supply.
Bronze, Silver, Gold and Platinum have standards that apply to both ~115 and ~230V supplies and represent incremental improvements in efficiency over the basic 80Plus standard.
80Plus Titanium is solely tested across ~230V, though it still represents a high level of quality and efficiency regardless of your location.
From a simplistic perspective, it gives you a good idea of the quality of components and the standards of production, but it's worth pointing out that all Gold (for example) rated PSUs are not equal. It is simply a measure of their efficiency, and while it can transfer benefits to longevity, quality and even cooling/acoustics, it's best to check out reviews from reputable sites to get a more complete picture.