Heavy libun means heating a utensil by fire until any ĥametz taste in it is incinerated. One indication that libun has taken place is that the utensil undergoing libun becomes so hot that sparks fly from it when it is brought into contact with iron. Another indication is that its outer layer peels off, or that it becomes red hot.
Light libun means heating a utensil by fire to the point that a piece of straw or thread placed on the opposite side of the utensil becomes blackened from the heat. For example, to kosher a frying pan through light libun one must place the pan over fire and then put a piece of paper on the frying surface. When the paper starts to become scorched, the pan has been koshered.
Light libun is not effective where heavy libun is required, because the objective of libun is to incinerate any taste absorbed into the utensil, and this is only achieved through heavy libun. However, light libun is more effective than hagala because it is more capable than hagala at extracting the taste of ĥametz from the utensil, and apparently it can also incinerate some of the absorbed taste. Sometimes, when it is uncertain if libun is necessary, one may suffice with light libun. Light libun has another advantage as well: if a utensil has crevices that are difficult to clean, hagala cannot kosher it, since hagala removes the taste absorbed into a utensil but cannot render kosher the residual food stuck in its grooves. However, if one performs light libun and aims the fire at the grooves, the residual food will be incinerated, and the utensil will be rendered kosher. Light libun can be performed by putting a utensil in an oven and heating it at the highest temperature for about half an hour.
It is worth noting, however, that some poskim rule leniently that a utensil that has absorbed ĥametz via fire does not necessarily require heavy libun. In their opinion, the principle of ke-bole’o kakh polto applies to the temperature at the time of absorption. Thus, if a utensil absorbed the taste of forbidden food at a temperature of 300ºC, it can be koshered at the same temperature, and if the absorption occurred at 200ºC, it can be koshered at 200ºC, even though it does not become red hot or give off sparks at this temperature. According to these authorities, a cooking tray that absorbed a forbidden taste in an oven can be koshered in that oven at the same temperature as the absorption. The practical halakha follows the majority opinion, namely, that a vessel that absorbed taste via fire and reached a temperature beyond yad soledet must be koshered by heavy libun. However, in extenuating circumstances and when there are other reasons to be lenient, we take the lenient opinion into consideration.
It should be emphasized that absorption through fire can only happen while the food is being cooked by the fire on the flame. For example, if one cuts a baked good while it is on the burner, the knife absorbs the taste of the food through fire. However, if the baked goods were first taken off the fire and then cut, even if the baked goods are dry, the absorption is considered mild, and the knife may be koshered through hagala.
According to most poskim, a utensil that absorbed taste by fire requires heavy libun, even if the utensil itself only reached yad soledet bo. However, there are authorities who are lenient, as noted above. See Arugot Ha-bosem §119 and Minĥat Yitzĥak 3:66. See also Kitzur SA op. cit. explanation 5 and Piskei Teshuvot 451:17.