All-or-nothing neuron activation means that the neuron is either on or off. When a neuron fires, it is called and action potential. There is no in-between state, and all action potentials have the same magnitude.
Neuronal activation is controlled by an electrical potential that is created through the separation of sodium and potassium ions across the neuron's membrane. The voltage measures the difference in this electric charge between the inside and outside of the cell.
At rest, the sodium ions are kept outside the cell and the potassium ions are kept inside the cell by the sodium-potassium pump. The resting potential is -70mV (millivolt), which means the charge inside the cell is 70 mV less than outside the cell.
When the neuron cell receives a signal, some of the sodium channels open, and the sodium ions rush into the cell. This changes the membrane potential. If the membrane potential passes a threshold level of -55mV, the neuron is fully activated. The activation is called an action potential. If the threshold is passed, more sodium channels open and the membrane potential reaches +30mV. At the end of the action potential, the potassium channels open and the potassium leaves the cell, returning the cell to a resting potential.
This process is called "all-or-nothing" because the cell is either on or off. If the threshold potential is met, then the neuron fires. If it is not met, there is no neuronal firing at all. In addition, the membrane potential always goes to +30 mV during an action potential. Thus, there is no difference in the magnitude of activation.