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.
 

Lets consider how a methyl group is involved in hyperconjugation with a carbocation centre.
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.)
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