Neutralisation, fundamentally, is the reaction of an acid and a base to give a neutral substance (water) and a salt.
The hydrogen ions from the acid and the hydroxide ions from the alkali join in equal concentrations to produce water molecules. What is left is the anion (negative ion) from the acid and the cation (positive ion) from the alkali, which also join to produce your salt.
HCl + NaOH -> H2O + NaCl
Acid + Base -> Water + Salt
When you take an indigestion tablet such as Rennies or Gaviscon, this same reaction happens in your stomach and oesophagus when you have acid reflux. The tablet neutralised any excess stomach acid to reduce heartburn.