A combustible substance can burn, and if nitrogen could burn, all life on earth would have been destroyed long ago. Nitrogen gas makes up some 78 percent of the earth's atmosphere. Roughly 21 percent of the atmosphere is oxygen, and if it could combine with nitrogen in a combustion reaction, there would be none left for organisms to breathe. Fortunately, that isn't the case. However, nitrogen can combust in certain unusual circumstances.
TL;DR (Too Long; Didn't Read)
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, it isn't nitrogen that burns, but magnesium. Nitrogen supports the combustion. Magnesium isn't found in nature because it much more readily reacts with oxygen. In the case of oxygen,
2 Mg + O2 --> 2MgO + energy
Nitrogen and Hydrogen
Hydrogen can react with nitrogen in certain circumstances. Once again, this is not a situation that occurs naturally because hydrogen ordinarily doesn't exist in elemental form. Even when you produce hydrogen artificially and react it with nitrogen to form ammonia, the nitrogen isn't being burned. It is the substance supporting the "burning." The equation for the reaction is:
N2 + 3H2 --> 2NH3
One of the special circumstances in which nitrogen can be combusted occurs during a thunderstorm. Lightning causes some nitrogen to react with oxygen to form nitric oxide:
N2 + O2 --> 2NO
and nitrogen dioxide:
N2 + 2O2 --> 2NO2
These reactions happen because lightning creates enormous pressures and temperatures as high as 30,000 degrees. Nitrogen and oxygen lose their electrons under such circumstances and become ions. Sometimes they will regain their electrons, but sometimes they combine and creating oxides. The oxides, in turn, can combine with moisture in the air and fall as rain, enriching 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 would start a fire which would burn out of control and which could quickly consume earth's forests. Nitrogen tempers oxygen's ability to support combustion, but it is not abundant enough to create a lack of biologically necessary oxygen.