Nugget is an Colonial military term to describe pilot trainees. Like many terms in the new Battlestar Galactica series, "nugget" is carried over from present day American military slang.
Please note that "nugget" should not be confused with "rook" or "rookie." The later term applies to a person who as completed their training and qualifications, yet is still inexperienced.
Kara Thrace is assigned the task of flight instructor to train a batch of potential Viper pilots after seven are killed in a freak accident (Act of Contrition). There are originially 8 nuggets, but Chuckles dies attacking a Cylon tylium refinery (The Hand of God). According to the SciFi.com official website, after the events of "The Hand of God", there are 5 surviving nuggets.