Lewis acids and bases are defined in terms of electron pair transfers. A Lewis base is an electron pair donor, and a Lewis acid is an electron pair acceptor. An organic transformation (the creation of products from reactants) essentially results from a process of breaking bonds and forming new ones. This process basically amounts to electron pair transfers. Ionic mechanisms involve electron pair transfers and are therefore described by the Lewis acid-base theory.
The Lewis definition implies the presence of high electron density centers in Lewis bases, and low electron density centers in Lewis acids. In a reaction between a Lewis acid and a Lewis base the electron pair donated by the base is used to form a new sigma bond to the electron deficient center in the acid. The identification of Lewis bases follows basically the same guidelines as the identification of Bronsted bases. They frequently contain atoms that have nonbonding electrons, or lone pairs. On the other hand, Lewis acids frequently contain atoms with an incomplete octet, a full positive charge, or a partial positive charge.
Water is an example of a Lewis base. Carbocations are examples of Lewis acids. When water reacts with a carbocation as shown below, one of the electron pairs from oxygen is used to form a new sigma bond to the central carbon in the carbocation. As with Bronsted acid-base reactions, curved arrow are used to indicate the movement of electron pairs during the reaction process. The arrow always originates with the Lewis base and moves towards the area of electron deficiency in the Lewis acid.
To avoid confusion between the Lewis and the Bronsted definitions of acids and bases, Lewis bases are sometimes called nucleophiles, and Lewis acids are called electrophiles. In the example above, water acts as a nucleophile (donates electrons), and the carbocation acts as an electrophile (receives electrons).
Since Bronsted acids and bases are a subcategory of the more encompassing Lewis definition, it can be said that most Bronsted bases are also nucleophiles, and that the proton is a Lewis acid, or an electrophile. There are however some subtle differences to keep in mind.