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From Citizendium, the Citizens' Compendium

Lewis acids are imporant chemicals used to catalyze or promoter reactions. A Lewis acid is a chemical that can accept a share of an electron pair that is donated by a Lewis base. Although Bronstad-Lowery acids are Lewis acids, most Lewis acids are not Bronstad-Lowery acids, that is, they do not give off a proton. A more complete discussion of Lewis acids and Lewis bases can be found at Lewis acid-base theory. Lewis acids can accept a share of an electron share either because they have an incomplete valence shell, as does AlCl₃ or BF₃ for example, or because the metal can be increase its valence, as can happen with SnCl₄.