For a pi-bond, p-orbitals overlap in a sidewise manner.
Covalent bonds are formed by the overlapping of atomic orbitals. There are two types of covalent bonds:
Sigma bonds are a result of the head-to-head overlapping of atomic orbitals.
Pi bonds are formed by the lateral or the sidewise overlap of two atomic orbitals.
In pi-bond, the overlap of atomic orbitals occurs in a direction perpendicular to the internuclear axis.
During the formation of π bonds, the axes of the atomic orbitals are parallel to each other whereas the overlapping is perpendicular to the internuclear axis as shown below: