hyperconjugation
/ HY-per-con-ju-GAY-shun /
Why is a tertiary carbocation more stable than a primary one, even though both look like they just have an empty pocket on carbon? The answer is hyperconjugation: nearby ordinary bonds quietly lend a bit of their electron density to the electron-hungry center. It is like neighbors passing food to someone who is short at the dinner table, without anyone formally moving seats.
More precisely, the electrons in an adjacent C-H or C-C sigma bond can overlap with the empty p orbital of a carbocation (or with the half-filled orbital of a radical). The pair of bonding electrons spreads slightly into the empty orbital, sharing its electron density and lowering the energy of the system. The more such neighboring bonds there are, the more donors are available, which is exactly why a tertiary cation (with three carbon neighbors offering many C-H and C-C bonds) is far happier than a primary one (with only one). Unlike ordinary resonance, which delocalizes pi electrons or lone pairs, hyperconjugation delocalizes the electrons of sigma bonds, which is why it is sometimes called 'no-bond resonance'.
Hyperconjugation is the hidden hand behind several rules students memorize. It explains the carbocation and radical stability order, why more substituted alkenes are more stable, and ultimately why Markovnikov addition prefers the more substituted carbocation. It is usually a smaller effect than full resonance, but it is real and it tips many close decisions about which product or intermediate dominates.
The tert-butyl cation (CH3)3C+ has nine C-H bonds positioned to donate into its empty orbital, giving it many hyperconjugative donors; a primary cation has far fewer, which is why it forms so reluctantly.
More neighboring C-H and C-C bonds means more hyperconjugation and a more stable cation.
Hyperconjugation delocalizes sigma-bond electrons and is usually weaker than true resonance, which delocalizes pi electrons or lone pairs; both stabilize, but they are not the same mechanism.