# What is the physical significance of the overlap integral?

What is the physical significance of the overlap integral in the covalent bond formation (say, the $H_2$ molecule)?

as far as I can understand, even if the overlap integral is zero, the Heitler-London theory of $H_2$ atom, it still admits a lower energy state compared to the total energy of two isolated H-atoms.

What is the significance of the following statement from Wikipedia?

In chemical bonds, an orbital overlap is the concentration of orbitals on adjacent atoms in the same regions of space. Orbital overlap can lead to bond formation.

Is it necessary to have non-zero orbital overlap for bond formation? Or does it suffice to have a lower energy level (compared to the total energy of two isolated H-atoms) to say a bond is formed?