The axolemma is the membrane of a neuron's axon. It is responsible for maintaining the cell's membrane potential, and it contains channels through which ions can flow. This changes the voltage inside the axon and can depolarize or hyperpolarize the cell. Adequate depolarization will lead to an action potential, which will travel down the axon in a self-propagating manner, as more ion channels open due to stimulation by the influx of positive ions.
If the axolemma is damaged, it becomes unable to perform its vital role of maintaining the concentration gradient of ions on the outside of the cell. When these ions rush down their gradient into the cell, they can cause a number of different cellular processes that lead to cellular damage and sometimes death.