A voltage-gated ion channel is an ion channel whose probability of being open depends on the membrane potential.

This creates a feedback link:

membrane voltage changes
        ↓
channel gating changes
        ↓
ion conductance changes
        ↓
ion flow changes membrane voltage

Because voltage controls channels and channels control voltage, excitable membranes can produce rapid regenerative responses.

Depolarization and hyperpolarization

A membrane depolarizes when its voltage becomes less negative or more positive. It hyperpolarizes when its voltage becomes more negative.

Opening a selective ion channel tends to move the membrane potential toward that ion's equilibrium potential. Thus opening a Na$^+$-selective channel in a cell whose $E_{Na}$ is strongly positive usually depolarizes the membrane, while opening a K$^+$-selective channel when $E_K$ is more negative usually drives the voltage in the opposite direction.

Activation and inactivation are different

Many voltage-gated channels do not simply switch between permanently closed and permanently open states.

A channel can undergo activation, entering a conducting state after a voltage change, and later inactivation, entering a nonconducting state even while the activating voltage remains.

For a common voltage-gated Na$^+$ channel pattern:

resting closed
   ↓ depolarization
open
   ↓ delayed inactivation
inactivated
   ↓ repolarization and recovery
resting closed

Voltage-gated K$^+$ channels often activate more slowly and help return the membrane toward negative voltages.

Positive and negative feedback

If depolarization opens Na$^+$ channels and Na$^+$ entry causes further depolarization, the result is positive feedback.

If delayed K$^+$ channel opening drives the voltage back toward $E_K$, that contributes a restoring influence.

Electrical excitability therefore does not come from voltage alone. It emerges from the voltage dependence, ion selectivity and timing of channel gating.