There are a few important distinctions to be made when considering the meaning of Kirchhoff's radiation law. Firstly, it describes only thermal or black-body radiation, but these two terms themselves are not always used as synonyms as I'm using them here. So this is one point of confusion.
People who work in the field of quantum optics tend to use "thermal spectrum" as a shorter substitute for "black-body spectrum." A true black-body spectrum is only present when the body in question is in radiative equilibrium with its surroundings. People other than quantum optics theorists consider thermal radiation to be electromagnetic radiation emitted due to an object's temperature, with no requirement of equilibrium.
So lets say "thermal spectrum" refers to a true black-body spectrum, and "thermal radiation" refers to any radiation produced by an object due to its temperature. Thermal radiation in this sense has a spectrum that is nearly identical to the black-body spectrum.
So: Let's say "thermal radiation" is light or other electromagnetic radiation being emitted by an object solely due to the object's temperature, and that this radiation has an approximately "thermal spectrum," and not worry about it not being exactly a black-body spectrum.
People who work in the field of quantum optics tend to use "thermal spectrum" as a shorter substitute for "black-body spectrum." A true black-body spectrum is only present when the body in question is in radiative equilibrium with its surroundings. People other than quantum optics theorists consider thermal radiation to be electromagnetic radiation emitted due to an object's temperature, with no requirement of equilibrium.
So: Let's say "thermal radiation" is light or other electromagnetic radiation being emitted by an object solely due to the object's temperature, and that this radiation has an approximately "thermal spectrum," and not worry about it not being exactly a black-body spectrum.
There are three common sources of visible thermal radiation that I can think of: the sun, incandescent light bulbs, and heating elements on electric stoves and ovens. The objects we see illuminated by the sun and incandescent bulbs preferentially absorb or reflect different parts of the spectrum, so when we look at the objects around us we don't see light that has a thermal spectrum. We see whatever regions of the spectrum the objects reflect. And you should see the spectral composition of sunlight at earth's surface section of the Wikipedia entry on sunlight for more info on the spectrum of visible light we normally observe from the sun.
Every "body" and everybody does produce some type of thermal radiation, however. Usually, it's not in the visible spectrum. Near-black-body radiation is produced by objects that have the same temperature as their surroundings. When we're in a room held at constant temperature--which is usually the case--the temperature of the walls of the room and the air in the room is about the same. This walls are producing very low frequency thermal radiation.
We warm-blooded creatures produce our own heat, and thus are not in equilibrium with our surroundings. Like other "hot" objects that are sources of their own heat, including the three mentioned above, we produce thermal radiation.
So the take-home message about thermal radiation is that a lot of care and effort go into producing an ideal absorber-radiator whose thermal radiation has the black-body spectrum. One way of producing such a spectrum is the radiation-in-a-box method, which I've discussed previously here and will be discussing again.
See this site for a thermal spectrum graph that changes as you enter different temperatures. If you enter room temperature of about 300K the graph shows no spectrum because the emissive power is so low that it doesn't register on the scale of the graph. (Okay, 300K is a lower temp than the slider scale allows, but the interactive nature of this particular site is worth trying out.)
Thermal and black-body radiation are most often described in terms of emissive power: the rate of emission of electromagnetic energy per unit area of the emitting object, expressed as a function of the temperature of the body and the wavelength (or frequency) of the radiation. But in discussing Kirchhoff's law, we can also talk about coefficients of emission and absorption, and it's often not clear whether a coefficient or emissive power or some combination of the two is being discussed. For instance:
Every "body" and everybody does produce some type of thermal radiation, however. Usually, it's not in the visible spectrum. Near-black-body radiation is produced by objects that have the same temperature as their surroundings. When we're in a room held at constant temperature--which is usually the case--the temperature of the walls of the room and the air in the room is about the same. This walls are producing very low frequency thermal radiation.
We warm-blooded creatures produce our own heat, and thus are not in equilibrium with our surroundings. Like other "hot" objects that are sources of their own heat, including the three mentioned above, we produce thermal radiation.
So the take-home message about thermal radiation is that a lot of care and effort go into producing an ideal absorber-radiator whose thermal radiation has the black-body spectrum. One way of producing such a spectrum is the radiation-in-a-box method, which I've discussed previously here and will be discussing again.
See this site for a thermal spectrum graph that changes as you enter different temperatures. If you enter room temperature of about 300K the graph shows no spectrum because the emissive power is so low that it doesn't register on the scale of the graph. (Okay, 300K is a lower temp than the slider scale allows, but the interactive nature of this particular site is worth trying out.)
Thermal and black-body radiation are most often described in terms of emissive power: the rate of emission of electromagnetic energy per unit area of the emitting object, expressed as a function of the temperature of the body and the wavelength (or frequency) of the radiation. But in discussing Kirchhoff's law, we can also talk about coefficients of emission and absorption, and it's often not clear whether a coefficient or emissive power or some combination of the two is being discussed. For instance:
"Kirchhoff's law of radiation A law stating that the emissivity of a body is equal to its absorptance at the same temperature"
--A Dictionary of Physics, Oxford University Press, 2nd edition, 1996.
This unhelpful definition says what is often said in regard to Kirchhoff's radiation law, that a good absorber of radiation must also be a good emitter. It may also make you wonder "What's the point?" We have equal emission and absorption of radiation as a required equilibrium condition, so in this sense it's a circular definition. Also, the most interesting thing about Kirchhoff's law is its universal applicability. It applies to all materials. A definition needs to take that into account. (There is a more recent definition given at the Oxford dictionary of physics website, but the newer part of the definition is not readily viewable.)
The Wikipedia definition of Kirchhoff's radiation law was updated recently and gives the best definition I've seen. Planck himself calls it the law of proportionality of the emissive to the absorptive power. The coefficient of absorption mentioned in the Wikipedia definition (and shown in the Russian encyclopedia definition in my previous post) provides this proportionality.
One more thing. You may be wondering about the universal nature of Kirchhoff's law--that it applies to all materials--and how it can apply materials that just catch on fire or melt when they get very hot. Wood and plastic should immediately come to mind. Kirchhoff's law still applies to these within the range of temperatures where the material isn't beginning to change its molecular structure due to being heated. That's why viewing thermal radiation in the higher temperature region, where the material becomes red hot, requires some kind of metal that can survive being heated to high temperatures.
