Infante (masculine) or infanta (feminine), also anglicised as infant, was the title and rank given in the medieval European kingdoms of Aragon, Castile, Galicia, Navarre, León, and Portugal to a son or daughter, and to a grandson or granddaughter in the male line of a reigning monarch (and also to a princess's children if she was the heir apparent to the throne), and their woman consorts. Male consorts had not, and have no right to the title, style and rank.
The name derives from the same root as "infant," but this means simply "child" in Romance languages (cfr. French Enfants de France), and in this case indicates that the Infante or Infanta is the child of the monarch. Like the Enfants de France, all Infantes in the different kingdoms were and are always royal princes, in the general meaning of the word.
Afterwards, the word Infanta emerged in Portugal as a feminised form applied to the Portuguese princesses after the 16th and 17th centuries. Also, after Edward of Portugal, in the 15th century, the heir apparent and his older son, or daughter, were styled just as "Prince" and "Princess". The first Prince in Portugal was the future Afonso V, his eldest son, maybe adopting the French royal style by an English influence brought by queen Philippa of England.
After the ascension of the House of Braganza to the royalty, it was added the title "Most Serene" (Sereníssimo) to the title of Infante - as well as Sereníssima to Infanta -, since the complete name of this house was "Most Serene House of Braganza" (Sereníssima Casa de Bragança), a style granted by the Pope. The style, however, does not seem to be used with the title of Prince Royal.
The current Infantes of Portugal (presently a republic) are close relatives of Duarte Pio, Duke of Braganza, head of the Portuguese Royal House:
Afonso de Santa Maria, Prince of Beira, Duarte Pio eldest son, as heir apparent to the Portuguese Royal House, is styled Prince of Beira, not Infante.
The current Infantas of Spain are:
Carlos de Borbón, Duke of Calabria and King Juan Carlos' cousin, also holds the title of Infante of Spain.
Prince Felipe, son of King Juan Carlos, as heir apparent to the Spanish throne, is styled Prince of Asturias, not Infante.