take hyperconjugation to an aromatic system, like benzene. Consider toluene (benzene substituted with a methyl group). Remember that benzene is aromatic and has a pi-system. The carbons on the ring are sp2-hybridized and there is significant overlap of the p-orbitals and pi-electrons. Well, consider that there is rotation about the methyl group and when one of the C-H sigma bonds of methyl group come into close alignment with the p-orbitals, the electron density in the sigma bonds can overlap with the pi-system, resulting in the donation of electron density into the aromatic ring. Thus, alkyl groups function as both o,p-activators and electron-donating groups (EDG) in electrophilic aromatic substitution. Naturally, hyperconjugation doesn't have as significant an effect as, say, the donation of an available lone pair of electrons in the nitrogen of aniline into the pi-system, but it is significant enough to lend additional stabilization in EAS.

The above explain the effect of alkyl substitution in EAS and in the stabilization of carbocation systems quite well. However, we should also take the time to note more generically, that the second often-cited reason for electron-donating effects of alkyl groups falls into the category of inductive effects. These effects are transmitted through the sigma system (sigma bonds) and are quite distance-dependant (effects decrease with distance). Essentially, inductive effects work by the shifting of electron density in response to differences in electronegativity between two entities in a molecule. The greater the difference in electronegativity, the bigger the polarization of electron density in the molecule. There are plenty of electrons in the sigma system of alkyl groups that can be polarized and "transmitted" when inductive effects come into play.