What does this equation mean?

The model’s core equation describes membrane current as the sum of capacitive, sodium, potassium, and leak components: $C_m \frac{dV}{dt} = -\bar{g}_{Na} m^3 h (V - E_{Na}) - \bar{g}_K n^4 (V - E_K) - g_L (V - E_L) + I_{ext}$. where m , h , and n are voltage- and time-dependent gating variables each obeying their own first-order kinetics. This is worth stating in full because it is the paradigm the rest of the field either extends or reacts against: a biophysical mechanism, expressed as a dynamical system, fit to directly measured current, with no free parameter standing in for an unmeasured process. It is why the model is still taught unmodified, and why its two authors and John Eccles shared the 1963 Nobel Prize in Physiology or Medicine. It is also, strictly, a model of one excitable membrane, not of a circuit, a computation, or a behavior — the questions that would define the next seventy years were exactly about what happens when this unit is multiplied by billions and wired into structure.