The acetylene molecule features a linear #H-C-C-H# vector in which participate ALL the valence electrons possessed by hydrogen (1 electron) and carbon (4 electrons) participate. So we have 10 electron to distribute....and these all end up residing in bonding orbitals.
To borrow from valence bond representation, 2 electrons from carbon participate in the linear #sigma-C-C# and the #2xxC-H# bonds; the remaining electrons required for the #2xx# terminal #sigma-C-H# bonds come from the hydrogen, i.e. #dotH#; i.e. we form #3xxsp# hybrid bonds for each carbon centre.
The two electrons remaining on carbon are perceived to be unhybridized, and these are formally #p_z# and #p_y# orbitals. These overlap in a #pi# interaction above and below the plane....
The electron density BETWEEN the carbon nuclei, negate nucleus, nucleus repulsion, and allows a very short #C-C# bond length of approx. #1.2xx10^-10*m#. This is to be compared to the #C-C# bond lengths of #1.35xx10^-10*m#, and #1.54xx10^-10*m# observed for #"ethylene"# and #"ethane"#, #H_2C=CH_2#, and #H_3C-CH_3# respectively. Dinitrogen, #N-=N#, another #sp# interaction also has a short bond of #1.10xx10^-10*m#.
