A regent, from the Latin regens "one who reigns" is anyone who acts as head of state, especially if not the monarch (who has higher titles). In a monarchy, a regent usually rules due to the actual monarch's absence, incapacity or minority, and may also be elected to rule during the sede vacante when the royal line has died out.
Thus, in France, between 1060 and 1066, during the minority of Philip I, his mother Princess Anne of Kiev acted as Regent. In 1552, during the reign of Henri II his queen, Catherine de Medici acted as Regent when the king left the kingdom on a military campaign to Metz in 1552. Again, on Henri's death in 1559, Catherine acted as Regent for their son, Francois II, and on his death, for his brother and successor, Charles IX.
In Scotland a serial regency occurred after the (hasty) departure of Mary Stuart to England in 1568. First James Stuart, Earl of Moray, ruled in her absence. After her death (execution at the hands of the Protestant English, she being a Catholic), first James, then Matthew, Earl of Lennox, then John Erskine, Earl of Mar, and then James Douglas, Earl of Morton, acted as regent for James VI during his minority.
Regents in the SCA
In the SCA, a regent is generally appointed when there is no current royal head of a group, i.e. no king or queen. There may be many reasons for the lack of royalty, like death or infringements of the Society's regulations, but the regent will normally help organise a crown tournament to decide a new king and queen. The regent does not have the power to change kingdom laws and give out awards. The regent's appointment ends with the coronation of new monarchs.