Why does the power go out in thunderstorms?

Probably because the lightning has struck an electric wire somewhere

two main reasons: power surge from strikes overloads a system and either fries a connection or kicks a circuit breaker; and wires
 get hit by tree limbs being pushed around by the strong wind, either breaking the wire, grounding it, or short circuiting across two lines, the latter two leading to a fused system someone or a circuit breaker cutting the power to protect the system from damage.