Why are pi bonds formed?

There is only one s orbital in any given energy level. Sharing the S orbital creates only one bond. To make a double bond the p bonds must be used.

The sharing of p orbitals creates pi bonds.

For example #N2# has three bonds. The triple bond requires the sharing of the one S orbital and two P orbitals . The S orbitals overlap directly forming a covalent bond. The two sets of p orbitals overlap side by side creating the pi bonds, which are also covalent bonds

Consider the formation of ethylene, #"H"_2"C=CH"_2#.

The #"C"# atoms are #sp^2# hybridized.

The #"C-C"# σ bond is formed by the overlap of the #"C"# #sp^2# orbitals, and the #"C-H"# σ bonds are formed by the overlap of the #"H"# #1s# orbitals with the #"C"# #sp^2# orbitals.

This leaves an unhybridized p orbital containing one electron on each #"C"# atom.

When you have two #p# orbitals on adjacent #"C"# atoms, they can overlap sideways to form a region of electron density that is not directly between the two nuclear centres but which still contributes to bonding.

We call this a π bond.

It forms because the π electrons are as close as they can get to the two nuclei and are therefore in their lowest energy state.

A π bond can only form only after a σ bond has already formed. It is always part of a double or triple bond.