The Labile Carbon is also known as the 'Rapid Cycling Carbon' and its composed of all the Soil Organic Matter that is dead and actively decomposing. It's benefit to the soil is that it provides a source for minerals that are being recycled as potential plant nutrients, so in a sense it's Nature's fertilizer.
Active Carbon also known as Reactive Carbon is more complex than the Labile Carbon in that its composed of all the dead and actively decomposing organic matter plus all the living soil microbial community that will eventually die and begin decomposing. For example, the hyphae of mycorrhizae only live about 5 to 7 days before they die and start to decompose, while the fungus organism itself may live far longer.
Recalcitrant Carbons are the Humic substances made up of complex organic chemistry, some of which is inert and some of which is very reactive and are powerful biologics, such as the Humic Acids. Recalcitrant Humic substances are known in laymen terms as Humus. These organic compounds are rich in carbon and made up of strong chemical bonds that resist breaking, therefore they persist in a soil for a long time. Clay particles and Humic Acids combine and make what is called a Clay-humus domain, which contributes to holding the soils structure together in macroaggregates. The Clay-humus domain also helps to hold the nutrients in a Cation Exchange Capacity format that keeps them available to plants at all time. Also helping to hold the macroaggregates together are the living roots and living hyphae of the plants and mycorrhizae along with the glycoproteins called Glomalin, a glue like substance leftover from the decay of the mycorrhizal hyphae. The significance of addressing the importance of living roots, hyphae and glomalin in the same breath as the Recalcitrant Carbons and Humic Acids is the issue of how tillage, plowing and rototilling damage the structure of soil. That activity kills the Active Carbon components of roots and hyphae, interrupting the production of glomalin, which combined causes a loss of macroaggregates, breaking everything down into microaggregates, which is not good!
Michael Martin Meléndrez