What is hyperconjugation?

Hyperconjugation is the stabilising interaction that results from the interaction of the electrons in a s-bond (usually C-H or C-C) with an adjacent empty (or partially filled) p-orbital or a p-orbital to give an extended molecular orbital that increases the stability of the system. Based on the valence bond model of bonding, hyperconjugation can be described as "double bond - no bond resonance" but it is not what we would "normally" call resonance.
Let's consider how a methyl group is involved in hyperconjugation with a carbocation centre.      interaction of a methyl group
First we need to draw it to show the C-H s-bonds.
Note that the empty p orbital associated with the positive charge at the carbocation centre is in the same plane (i.e. coplanar) with one of the C-H s-bonds  (shown in blue.)     look at the sigma bonds
This geometry means the electrons in the s-bond can be stabilised by an interaction with the empty p-orbital of the carbocation centre.

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