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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 is described as "double bond - no bond resonance" but it is not what l resonance,

Hyperconjugation is a factor in explaining why increasing the number of alkyl substituents on a carbocation or radical centre leads to an increase in stability.

consider methyl group involved in hyperconjugation with a carbocation centre.

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
This geometry means the electrons in the s-bond can be stabilised by an interaction with the empty p-orbital of the carbocation centre.

The stabilisation arises because the orbital interaction leads to the electrons being in a lower energy orbital

the C-C s-bond is free to rotate, and as it does so, each of the C-H s-bonds in turn undergoes the stabilising interaction.
So the ethyl cation has 3 C-H s-bonds that can be involved in hyperconjugation.
The more hyperconjuagtion there is, the greater the stabilisation of the system.
for example, the t-butyl cation has 9 C-H s-bonds that can be involved in hyperconjugation. Hence (CH3)3C+ is more stable than CH3CH2+
The effect is not limited to C-H s-bonds, appropriate C-C s-bonds can also be involved in hyperconjugation.

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