= Solution
In the <Hodgkin-Huxley model>, $V$ is the <membrane potential>, the <voltage> inside the axon relative to outside. The <space clamp> assumption makes it spatially uniform. The gating variables lie between zero and one: $m$ describes <sodium> activation, $h$ describes availability against <sodium> inactivation, and $n$ describes <potassium> activation. Thus large $h$ means channels remain available, not that inactivation is strong.
The left side $C_m\dot V$ is capacitive <electric current> per unit membrane area. The imposed $I$ is inward-positive applied <electric current>. The other terms are outward-positive ionic <electric currents>: <sodium> with <electrical conductance> $g_{Na}m^3h$, <potassium> with conductance $g_Kn^4$, and a passive leak with conductance $g_L$. Each current is its conductance times the difference between $V$ and the corresponding <reversal potential> $V_{Na}$, $V_K$ or $V_L$. The coefficients $g_{Na},g_K$ are maximal conductances; the gate factors represent <independent permissive gates in an ion channel>.
For each gate, $k_\infty(V)$ is the equilibrium opening/availability fraction at fixed <voltage> and $\tau_k(V)>0$ its <exponential relaxation time>. The equation follows from <two-state ion-channel gating>: if $\dot k=\alpha_k(V)(1-k)-\beta_k(V)k$, then
$$
\boxed{k_\infty=\frac{\alpha_k}{\alpha_k+\beta_k},\qquad\tau_k=\frac1{\alpha_k+\beta_k}.}
$$
<Voltage> feedback couples these otherwise elementary gating equations to the <membrane potential> and produces <action potentials>.
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