A combustible substance is a substance that can be burned. Usually this means burned in the open air or atmosphere. If nitrogen could burn, all life on earth would have been destroyed long ago, as nitrogen gas makes up some 78 percent of the earth's atmosphere, with roughly 21 percent of the remaining 22 percent of earth's atmosphere being oxygen. The oxygen in air would have burned up the nitrogen in the air.
The Simple Answer
The obvious and simple truth is that nitrogen is not combustible under ordinary circumstances. In fact, the National Fire Protection Association has given nitrogen a flammability rating of zero. There are certain special situations, however, that require special consideration.
Nitrogen and Metals
Under very special conditions, nitrogen can be consumed as if it was supporting the combustion of other substances. For instance, it can combine with certain unusually reactive metals not ordinarily found in nature in elemental form, such as magnesium.
3 Mg + N₂ ' Mg₃N₂
In this instance, rather than nitrogen being burned, it is the magnesium that is combusted, with nitrogen supporting the combustion. Magnesium isn't found in nature because it much more readily reacts with oxygen. In the case of oxygen,
2 Mg + O₂ ' MgO
Nitrogen and Hydrogen
Hydrogen can be made to react with nitrogen. Once again, this is a situation not found in nature. Hydrogen ordinarily doesn't exist in elemental form. Even when it is artificially made and it is reacted with nitrogen, the nitrogen isn't being "burned". Rather, it is the substance supporting the "burning." Thus,
N₂ + 3 H₂ ' 2 NH₃
There are also special circumstances in which nitrogen can be combusted. One of these is during a thunderstorm. Lightning causes some nitrogen to react with oxygen, forming oxides. Thus,
N₂ + O₂ ' 2 NO
N₂ + 2 O₂ ' 2 NO₂
This is because lightning creates artificially enormous temperatures and pressures. Temperatures under such circumstances reach as high as 30,000 degrees. This ionizes nitrogen and oxygen, stripping them of electrons. Sometimes they will regain their electrons, with no net result. At other times, they combine together, creating the oxides as shown above. The oxides can react, in turn, with moisture in the air. Some of that water comes to earth in the form of raindrops, which enriches the soil.
It is really a good thing that the majority of earth's atmosphere consists of the ordinarily non-combustible nitrogen. If all the atmosphere was oxygen, the first spark could start a fire which would burn out of control and which could quickly consume earth's forests and other combustibles. The nitrogen dilutes oxygen's efficacy at supporting combustion, while not being so abundant that biologically needed oxygen is lacking.