Literally, this phrase means 'New Man' in Latin
In the Roman Republic there were two ways of becoming a member of the nobility: the first way was the most common as well as the fastest and surest way of becoming a Patrician, and that's simply to be born to a noble family. The second way was to be elected to the position of Consul or Praetor. Those people who became of the Nobilitas, due to their service and not to their birth were called (usually in disdain) Novi Homines, New Men.
One might think that it shouldn't be too hard then to become a nobleman, one simply had to run for office, however the chronicles show us that in the 300 years that the Roman Republic existed (I don't consider the nominally republican government that served under the emperors really republican), and while each year two Consules and several Praetores were elected, only 15 men became Novi Homines!
That was a result of the fact that early on in the history of the Republic a group of 15 noble families took over those positions and no one could be elected to them without their approval. As a result non-nobles served as Consules and Praetores only in times of crises, when the Republic needed trully capable men, and not just well-born ones.
Marcus Tullius Cicero was probably the most famous Novus Homo in the Roman history.