Thermal radiation is energy given off (radiated) by a body as a consequence of its temperature exclusive of any energy transferred away from the body through conduction or convection. It is electromagnetic energy, and as such consists of photons emitted by the body - what is sometimes called blackbody radiation.

It is important because unlike convection and conduction it is the means by which an object can lose (transfer away) energy to another object(s) through a vacuum. Since every object in the universe has a finite temperature that is above absolute zero Kelvin (as far as we know), that means every object will emit thermal radiation which, if placed against a cold enough background, can be detected. Space itself has a temperature, the 'cosmic background radiation' which is in the microwave range and represents the thermal radiation of the universe itself.

As an object gets hotter, it will radiate more brightly. Not only that, but it will radiate at higher and higher frequencies as well. Planck's Law is used to determine what the emission frequency strength curve of an object is based on its surface temperature. In order to determine the peak of that curve, i.e. the wavelength on which the most energy is emitted, one can use Wien's Law (thanks filoraene!) which looks somewhat like this:

λmax Angstroms = 3 x 107 Angstroms / Temp ( Kelvin )

Some handy values of λ to know on the electromagnetic spectrum: visible light is (very roughly?) 4,000 to 7,000 angstroms, violet to red. ultraviolet light ranges from 10 to 4,000 angstroms, X-Rays from 0.1 to 10, and gamma rays below 0.1. The other way, infrared starts at 7,000, microwaves at 106 angstroms, and radio at 109.

NOTE: As anyone who knows anything about this subject can tell, I don't know much. This node is mostly intended to gall someone who *does* know about it into superseding it with a better version (hint hint hint)