A neutralization reaction is taking a solution that is either acidic or basic and adding a reagent of the opposite nature to bring the pH back to neutral (or near neutral). An excellent example is adding HCl and NaOH together in aqueous solution:
HCl + NaOH --> H2O + NaCl
The end result of adding the strong acid to the strong base is producing water with an ionic salt dissolved in it. A neutralization reaction is usually exothermic in nature, meaning the chemical reaction itself gives off heat. This occurs due to a change in the enthalpy levels between the products and the reactants. The reactants have a higher energy (enthalpy) in their chemical bonds than the products. In other words, the products (water and an ionic salt) are more stable and therefore in a lower energy state that the reactants. So when the higher energy reactants are transformed into the lower energy products, the resulting loss of energy (enthalpy) is given off as heat. This can be measured quantitatively using a device called a calorimeter. This is a reaction vessel that is encapsulated in a thermally protected water jacket. The heat given off by the reaction in the center transfers its heat to the surrounding water which is measured with a thermometer. There are sets of equations (in the link below) that can be used to measure the enthalpy change of the calorimeter reaction.