Explain $s{p^2}$ hybridization.

Hint: The hybridization is the intermixing of orbitals containing the same energy to form a new orbital. In $s{p^2}$hybridization, one s-orbital and two p-orbital combines to form a new $s{p^2}$ hybrid orbital.

Complete step by step answer:
Hybridization is defined as the mixing of two or more atomic orbits having the same energy to form a degenerated new orbital. When two atomic orbital join together to form a hybrid orbital, results in the redistribution of energy of the orbitals of atom to form orbitals of similar energy.
On the basis of types of orbital involved in the mixing to form new orbitals, the hybridization is classified as $sp$, $s{p^2}$, $s{p^3}$, $s{p^3}d$, $s{p^3}{d^2}$, $s{p^3}{d^3}$.
When one s-orbital and two p- orbital of same energy level combine to form three new orbits, the resulting hybrid orbital is $s{p^2}$ and the hybridization is also $s{p^2}$.
The mixture of s-orbital and p-orbital forms a trigonal planar geometry and the shape is trigonal planar. In this symmetry, all the three orbitals remain in the same plane and are placed at $120^\circ$ from each other. Each hybrid orbital is formed of 33.33 % s character and 66.66 % p character.
In trigonal planar shape, the central atom is linked with three other atoms.
The example of $s{p^2}$ hybridization is all boron compounds like $B{F_3}$ , $B{H_3}$ and all compounds containing double bonds like ethylene.

Note:
In $s{p^2}$hybridization, if two atoms are bonded with the central atom and one lone pair is present then the shape of trigonal planar geometry becomes bent.