What is Reciprocal lattice?

For a lattice of basis vectors $\mathbf a$, $\mathbf b$, $\mathbf c$ and cell volume $V$, the reciprocal lattice has basis vectors $\mathbf a^* = (\mathbf b\times\mathbf c)/V$, $\mathbf b^* = (\mathbf c\times\mathbf a)/V$, $\mathbf c^* = (\mathbf a\times\mathbf b)/V$, so that $\mathbf a\cdot\mathbf a^* = 1$ and $\mathbf a\cdot\mathbf b^* = 0$. Its node $\mathbf G_{hkl} = h\mathbf a^* + k\mathbf b^* + l\mathbf c^*$ is perpendicular to the planes $(hkl)$, and $|\mathbf G_{hkl}| = 1/d_{hkl}$.