Basis set orthonormality property

What does orthonormality of a basis set i.e. {χ_i} stand for? I am reading the Mulliken Population Analysis and there are integrals that are simplified by this property of basis sets and I can't quite catch what is it.

Fredrik
Staff Emeritus
$$\|u\|=\sqrt{\langle u,u\rangle}$$
$$\langle x_i,x_j\rangle=\delta_{ij}$$
where $\delta_{ij}$ is the Kronecker delta (=1 when i=j, and =0 otherwise).