Truly understanding triple bonds requires a closer look at what's going on with the crazy, unpredictable electrons that are involved.
Electrons buzz around an atom in particular shapes according to their energy level and distance from the nucleus. The organization of electrons around an atom is called the electron configuration, and the particular shapes inhabited by electrons are called electron orbitals. There are four shapes of electron orbitals, s, p, dand f. In triple bonds, the s and p orbitals are involved.
Each atom participating in the triple bond must shuffle electrons and orbitals around so that six electrons can be evenly shared. Each atom must first do some magic and fuse their outermost s orbital with a p orbital. This hybrid orbital is called sp and will contain two total electrons. As if it wasn't complicated enough, this bond is often referred to as a sigma bond. Each atom will then use the two remaining p orbitals to share electrons with the other atom. Electrons shared in p orbitals are called pi bonds.
A triple bond consists of one sigma bond and two pi bonds. The image shows how they are arranged between two nitrogen atoms. Together, the two dark green bands are one pi bond. The two light green bands are another pi bond. The orange band represents the sigma bond, made by overlapping sp orbitals.