A base is any substance that reacts with an acid to form a salt and water only. A salt is formed when the hydrogen ions of an acid are replaced by metal ions. The name of the salt depends on the acid. Hydrochloric acid makes chlorides, sulfuric acid makes sulfates and nitric acid makes nitrates.
Metal oxides and metal hydroxides are bases. For example, copper oxide reacts with sulfuric acid to form copper sulfate and water. Magnesium oxide reacts with nitric acid to form magnesium nitrate and water.
The word only matters in the definition. A metal carbonate is not a base, because when it reacts with an acid it forms a salt, water and carbon dioxide. A metal is not a base either, because it forms a salt and hydrogen.