(N/A) Hyperconjugation involves the delocalization of $\sigma$ electrons of a $C-H$ bond of an alkyl group directly attached to an unsaturated system (like an alkene or a carbocation).
$(a) \ CH_3-CH=CH_2$: The $\sigma$ electrons of the $C-H$ bond shift to form a $C=C$ double bond,and the $\pi$ electrons of the original $C=C$ bond shift to the terminal carbon.
Resonance structures: $CH_2^--CH=CH_2 \leftrightarrow H^+ \dots CH_2=CH-CH_2^-$.
$(b) \ CH_3-CH_2^+$: The $\sigma$ electrons of one $C-H$ bond shift to form a $C=C$ double bond,leaving the hydrogen as $H^+$.
Resonance structures: $CH_2=CH_2 \leftrightarrow H^+$.
$(c) \ CH_3-CH_2-CH_2^+$: The $\alpha$-carbon is the one adjacent to the positively charged carbon. The $\sigma$ electrons of the $C-H$ bond on the $\alpha$-carbon shift to form a $C=C$ double bond,resulting in the following resonance structures:
$CH_3-CH_2-CH_2^+ \leftrightarrow CH_3-CH=CH_2 \leftrightarrow H^+ \dots CH_3-CH^+=CH_2$.