Membrane stabilizing effects involve the inhibition or total abolishing of action potential

Action potential

In physiology, an action potential is a short-lasting event in which the electrical membrane potential of a cell rapidly rises and falls, following a consistent trajectory. Action potentials occur in several types of animal cells, called excitable cells, which include neurons, muscle cells, and...

 from being propagated across the membrane. This phenomenon is common in nerve tissues as they are the carrier of impulses from the periphery to the central nervous system

Central nervous system

The central nervous system is the part of the nervous system that integrates the information that it receives from, and coordinates the activity of, all parts of the bodies of bilaterian animals—that is, all multicellular animals except sponges and radially symmetric animals such as jellyfish...

. Membrane stabilization is the method through which local anesthetic

Local anesthetic

A local anesthetic is a drug that causes reversible local anesthesia, generally for the aim of having local analgesic effect, that is, inducing absence of pain sensation, although other local senses are often affected as well...

s work. They block the propagation of action potentials across the nerve cell thereby producing a nerve block.