Hyperconjugation and the stability of alkenes
Ordinarily without the contribution of the π* orbital, we would expect the interaction of two filled orbitals to be destabilising, in the sense that $E_2 &gt; E_1$ (as drawn in the diagram). This is the same rationale as why simple MO theory predicts the helium dimer to be unstable with respect to dissociation, for example.

It might be slightly unclear, but my interpretation of the text is that the empty π* orbital contributes a little bit to both MOs $\psi_1$ and $\psi_2$. This leads to a tiny stabilisation of both of these two MOs, such that the destabilisation $E_2$ is a bit smaller and the stabilisation $E_1$ a bit larger. Although it is not very obvious, you can see this from the figure.

It could probably have been made clearer by drawing extra dotted lines from the π* orbital to those MOs. My guess as to why Fleming hasn't done that is because he wanted to use dotted lines to illustrate the most significant orbital interactions (those between orbitals of similar energy). Note how he emphasises in the text that the σ and π* orbitals are not very close in energy (which implies that the interaction is small).