Broadly speaking, a vicar is anyone acting as an agent for a superior; hence its application in the Holy Roman Empire for local representative of the emperor; the word may come from the Persian vezir. We know it best, however, in its function within Christian ecclesiastics and get a sense of it in the word "vicarious."
Baldly put, a vicar is a representative.
Originally in the Catholic church, a vicar represented any ecclesiastic- this sense of the term dates vicars back to the earliest church. The role evolved over time, until the Pope began to use the title Vicarius Christi, the vicar of Jesus Christ, in the 8th century. Since then, vicars have taken different forms in Catholocism, including apostolic vicars, vicars capitular, judicial vicars, and vicars forane- all with different roles and powers.
In the Church of England, vicar is the standard term given to certain parish priests. Anglican clergy have been divided into rectors, vicars, and perpetual curates. This occurred along the lines by which they were remunerated: of the greater tithes of wheat, hay, and wood and the lesser tithes of the remained, the rector received both. The vicar received only the lesser tithe. A perpetual curate, on the other hand, depended on the support of the diocese. Historical changes have modified these distinctions until the term vicar can apply to nearly any clergy in the Church of England.
However, the Episcopal Church in the United States of America retains the distinction on monetary lines. That is, the priest of a self-sustaining parish is a rector, while the priest of a missional parish, fiscally reliant on the diocese, is a vicar.
Famous sons of vicars include Sir Francis Drake, Thomas Hobbes, and Samuel Taylor Coleridge.