A Lewis acid is an electron pair acceptor and a Lewis base is an electron pair donor. They can react with each another such that a covalent bond forms, with both electrons provided by the Lewis base.
Lewis acids have an unoccupied low-energy atomic or molecular orbital. Lewis bases have occupied relatively high energy atomic or molecular orbitals.
This is a more flexible definition of acids and bases than the more traditional Bronsted-Lowry definitions, which say that acids are species that donate a proton (H+), and bases are species that accept a proton.
The Lewis definition encompasses compounds that the Bronsted-Lowry definition says are acids or bases, and also encompasses compounds that do not donate protons, but still exhibit acid/base behavior.
Lewis acids and bases can be described as hard or soft.
Examples of Lewis Acids: H+, K+, Mg2+, Fe3+, BF3, CO2, SO3, RMgX, AlCl3, Br2.
Examples of Lewis Bases: OH-, F-, H2O, ROH, NH3, SO42-, H-, CO, PR3, C6H6.
Lewis Acid Example
An example of an acid/base reaction that can't be described by the Bronsted-Lowry definition is Al3+ in water.
Al3+ is a hard Lewis acid.
It reacts with water to produce an aqua complex Al(H2O)63+.
In this complex, the Al3+ accepts electron-pairs from six water molecules.
The water donates electron-pairs, so it is acting as a Lewis base.
In the traditional acid/base neutralization reaction of H+ and OH-, H+ is a Lewis acid because it accepts an electron pair from the OH-. Since the OH- donates an electron pair it is a Lewis base.