Why do action potentials travel in only one direction?

Action potentials travel in only one direction along an axon due to a brief refractory period that prevents depolarization from occurring in the direction from which the impulse came. 

Specifically, after an action potential occurs, the affected membrane patch enters a refractory period during which it cannot undergo another action potential. This refractory period is primarily caused by the inactivation of voltage-gated sodium channels at the peak of the action potential and continues through most of the undershoot period. Even if the membrane potential rises above the threshold, the inactivated sodium channels are unable to open. 

The slow closure of voltage-gated potassium channels makes it more difficult to depolarize the membrane even after the sodium channels are reactivated, further contributing to the refractory period. Thus, the refractory period ensures that action potentials only travel forward, from the cell body toward the axon terminal, preventing backward propagation.