Basically it has to do with the nature of double and triple bonds. In general, hybrid orbitals can participate only in the formation of sigma bonds, which are a along the internuclear axis (the imaginary line connecting the nuclei of the two atoms). Since there is only one internuclear axis, only one sigma bond is possible between two atoms. In order to form double and triple bonds, the atoms must form pi bonds which lie outside of the internuclear axis. Since pi bonds are formed from two parallel p orbitals, the atoms must leave unhydridized p orbitals to allow the formation of pi bonds. Therefore, ethylene, which contains a double bond, contains one sigma bond and one pi bond, so each carbon requires one unhybridized p orbital. Acetylene's triple bond is composed of one sigma bond and two pi bonds, requiring each carbon to have two unhybridized p orbitals.