The type of bonding can be explained in terms of orbital hybridization. In the case of acetylene each carbon atom has two sp orbitals and two p-orbitals. The two sp orbitals are linear with 180° angles and occupy the x-axis (cartesian coordinate system). The p-orbitals are perpendicular on the y-axis and the z-axis. When the carbon atoms approach each other the sp orbitals overlap to form a sp-sp sigma bond. At the same time the pz-orbitals approach and together they form a pz-pzpi-bond. Likewise, the other pair of py-orbitals form a py-py pi-bond. The result is formation of one sigma bond and two pi bonds.
In the bent bond model the triple bond can also formed by the overlapping of three sp3 lobes without the need to invoke a pi-bond.