Answer: They developed a model to explain the ionic conductances observed during initiation and conduction of the action potential.
Alan Hodgkin and Andrew Huxley were two English physiologists who pioneered some of the first experiments into modeling the function and behavior of neurons using electrophysiology. They initially worked collaboratively at the Physiological Laboratory (Cambridge) in 1935 using the frog sciatic nerve model, and later at the Laboratory of the Marine Biological Association (Plymouth) using the squid giant axon.
Although both sets of experiments were valuable, the squid giant axon studies allowed Hodgkin and Huxley to develop their mathematical model of conduction across a membrane.
They used concepts from physics to explain the workings of the cell membrane. For example, they are able to model the electrical properties of neurons using capacitors, resistors, and batteries.
The cell membrane, since it separates charge, acts as a capacitor. Ion channels allow for current flow, so they are resistors. Of the ion channels, there are two types that have different resistive properties. Voltage gated ion channels are modeled as nonlinear resistors, while leak channels are modeled as linear resistors. And lastly, there is the separation of ions, which represents the charge of a battery. These components are in parallel with each other.
Their work earned them a Nobel prize in 1963.