Potassium channels are special "gates" within the membrane that separates nerve cells (neurons) from the surrounding environment (the extracellular fluid). These channels are opened or closed depending on electrical or chemical stimuli. When they are open, they let charged potassium particles (ions) pass through them.
Potassium ions (K+) and sodium ions (Na+) flow between the neurons and the extracelluar fluid to set up the state of electrical charge potential when the neuron is at rest (the resting potential) and to release that potential when the neuron is sending a nerve impulse (the action potential). Sodium ions flow through other special gates called "sodium channels".
Potassium channels are opened immediately after the action potential has passed along the nerve. How sodium and potassium channels are involved in nerve transmission is dealt with in the section on the action potential.
There are two main types of potassium channel, voltage-gated channels and chemically-gated channels. Voltage-gated channels open or close in response to the surrounding electro-potential while chemically gated ones open and close in reponse to chemical stimuli. Dendrites, the branched filaments that receive nerve transmissions from other neurons, tend to have more chemically-gated potassium channels and fewer voltage-gated potassium channels by comparison with axons, the long extensions that send these transmissions on to other neurons.
See Action Potential.
Potassium Channel Links:
Ion Transport Tutorial
Basic Neuron Physiology
Genion Potassium Channels
Functions and modulation of voltage-gated potassium channels