quantum mechanics - What is the physical sense of the transition dipole moment?

So if the states are the same we achieve the expectation value of the dipole moment for a given state. I mean

$ \langle \mathbf{\mu} \rangle = \langle \psi \vert \hat{\mathbf{\mu}} \vert \psi \rangle$

But I don't feel the physical sense in the case of transition dipole moment when psi-functions on both sides are different

$\langle \psi_{1} \vert \hat{\mathbf{\mu}} \vert \psi_{2} \rangle$

Help me to understand, please.