One law of nature is that everything seeks a greater level of stability.
The ground state of an atom with 3 valence electrons is #s^2p^1# (such as boron). This is the most stable electron structure of the atom so far because the electrons are in the lowest energy formation.
Let's take boron as an example, with the #2s^2 2p^1# configuration.
When three identical atoms want to bond with boron, mixing the #2s# and two of the #2p# orbitals, and then moving both of the #2s# electrons into the newly-hybridized orbitals, the atom now has three unpaired electrons that can form three identical bonds.
Now, it can create a more stable, symmetric structure.
The #2s^2 2p^1# becomes #(sp^2)^3#. This allows boron to share all three of its valence electrons to, say, fluorine, allowing it to fill its outer shell while also accommodating for the fluorine's valence shell. This molecule is more stable than the initial free atoms, #"B"# and #3xx"F"#.
So by mixing one #s# and two #p# orbitals to form new #sp^2# orbitals that are totally symmetric about the internuclear axes, the central atom can combine with other atoms to achieve a more stable molecule with three properly-identical bonds.
