Molecules containing bonds of orders higher than one (i.e., double and triple bonds) contain #pi# bonds. For example, each molecule of ethene #"H"_2 "C" = "C" "H"_2# contains a carbon-carbon #"C"="C"# double bond.
Each neutral carbon atom contains four valence electrons. The atom undergoes a hybridization process that would result in three #sp^2# orbitals and one #2p# orbital before bonding to another carbon atom of an identical configuration and forming a carbon-carbon double bond.
As seen in the diagram, the #2p# orbital that is left half-filled and not hybridized is capable of overlapping with an equally half-filled and unhybridized #2p# orbital from another carbon atom.
The two #2p# orbitals overlap in parallel ("sideway") to the bonding axis between the two nuclei and the sigma bond from the overlapping of two #sp^2# orbitals. Note that each #p# orbital contains two petal-like electron clouds such that #"two"# regions of high electron density on opposite sides of the bonding axis (shown in blue in the second diagram) makes a single #pi# bond.
