To allocate favour or advantage to family or friends (e.g. giving your cousin a job rather than a better qualified stranger).
The origin is the Italian word nepotismo which comes from the Latin nepos for nephew. Notoriously, some less scrupulous Popes appointed their nephews as cardinals to maintain dynastic succession without flouting their vow of chastity.
For instance, Pope Callixtus III, head of the Borgia family, made two of his nephews cardinals; one of them, Rodrigo, later used his position as a cardinal as a stepping stone to the papacy, becoming Pope Alexander VI. Alexander then elevated Alessandro Farnese, his mistress's brother, to cardinal; Farnese would later go on to become Pope Paul III.Paul III also engaged in nepotism, appointing, for instance, two nephews, aged 14 and 16, as cardinals.
In 1692 Pope Innocent put an end to this practice in the Vatican but appointing what the Spanish call 'los tuyos' remained endemic in other spheres. Napoleon Bonaparte, for example, appointed his brother Louis, King of the Netherlands.
These days the nepotism usually takes more subtle forms. In US politics, for example, there are names that confer advantage (Gore/Bush/Clinton/Romney/Kennedy) but none guarantees a path to the presidency.