Local anaesthesia means a no pain sensation in a particular area supplied by a specific nerve. The correct term is local analgesia but commonly not used.
How does local anaesthetics prevent the conduction of dental pain?
Local anaesthetics inhibit the generation of electrical impulses and their conduction along the neuronal axon membrane, by reversible blockade of sodium ion channels.
There is a continuous imbalance of sodium and potassium ions between the cytoplasm of neurons and the intercellular fluid.
This is maintained at about 25 times more potassium intracellularly and 15 times more sodium in interstitial space.