The Brønsted-Lowry definition classifies acid-base reactions by proton transfer. The Lewis definition is broader and classifies them by electron-pair transfer.

A Lewis base donates an electron pair to form a new bond. A Lewis acid accepts an electron pair to form that bond.

For example, ammonia contains a lone pair on nitrogen and can donate it to a proton:

$$\mathrm{:NH_3+H^+\rightarrow NH_4^+}.$$

Ammonia is the Lewis base and $\mathrm{H^+}$ is the Lewis acid. This is also a Brønsted-Lowry acid-base reaction because a proton is transferred.

Lewis acid-base chemistry does not require proton transfer. Boron trifluoride, $\mathrm{BF_3}$, has an electron-deficient boron center: boron has room in its valence structure to accept an additional electron pair. Ammonia can donate its lone pair to boron:

$$\mathrm{BF_3+:NH_3\rightarrow F_3B!\leftarrow!NH_3}.$$

The new bond uses both electrons originally supplied by the donor. Such a bond is often called a coordinate covalent bond, although once formed it is an ordinary covalent bond in the resulting electronic structure.

Common Lewis bases possess available lone pairs or, in some cases, electron-rich multiple bonds. Examples include $\mathrm{OH^-}$, $\mathrm{Cl^-}$, water, ammonia and many oxygen- or nitrogen-containing molecules.

Common Lewis acids include positively charged species and neutral electron-deficient centers capable of accepting an electron pair. $\mathrm{H^+}$, many metal cations and molecules such as $\mathrm{BF_3}$ are examples.

Identifying the roles

In

$$\mathrm{AlCl_3+Cl^-\rightarrow AlCl_4^-},$$

the chloride ion supplies a lone pair and is the Lewis base. The aluminum center accepts the pair and is the Lewis acid.

Formal charge alone is not the definition: a neutral species can be a Lewis acid or base if its electronic structure provides an electron-pair acceptor or donor site.

Lewis acid-base reasoning provides a general language for bond formation. In organic chemistry, electron-pair donors acting at reactive sites are commonly described as nucleophiles, while electron-pair acceptor sites are described as electrophiles.