Neutralization reactions are ones in which one chemical reagent is added to another chemical reagent to remove its chemical potency or activity. This is most commonly seen in acid and base chemistry. Acids are defined as chemicals that donate protons and bases are defined as chemicals that accept (or react with) protons. A proton is a hydrogen cation (H+). So an acid can be neutralized with a base and a base can be neutralized with an acid. This can be very useful and effective since acid/base chemistry is usually very fast and the byproducts are usually inert or harmless (often forming simply water and a soluble salt). A common example of a neutralization reaction is a person taking an antacid for an upset stomach. The antacid is basically calcium carbonate (a mild base) that can neutralize (or react with) excess stomach acid to form carbon dioxide and water.
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