In a chemical double displacement reaction two compounds swap ions, effectively displacing each other to form two new compounds (aka double replacement reaction). For example:

One of the compounds formed is usually a precipitate, an insoluble gas that bubbles out of the solution, or a molecular compound, usually water.

A neutralization reaction is a specific type of double displacement reaction. Neutralization occurs when equal amounts of acid react with equal amounts of a base. A neutralization reaction creates a solution of salt and water. E.g.: