Disciple carries the same meaning as its Latin root discipulus: "pupil" or "student".
This also applies in the Biblical sense: several groups of people are identified as disciples, or students, of a teacher. The best known are certainly the 12 Disciples of Jesus, but Jesus had other noted disciples (e.g. Nicodemus, Joseph of Aramathea, Mary Magdalene, and Stephen). Other teachers of the New Testament also had disciples: John the Baptist had a large number (at least two of Jesus' disciples, John and James, were originally disciples of John's), and Paul of Tarsus had several notable disciples (e.g. Luke, Mark, Timothy).
Note that in the 1st Century Jewish culture, becoming a disciple to a teacher did not simply mean to learn from that person. True discipleship involved a commitment from both parties, much like a master-apprentice relationship. The magnitude of this commitment may be gleaned from the fact that the modern English word "discipline" (both in the sense of "a course of study", as well as "correction" or "rebuke") derives from the same root.
Although not termed as such, some relationships in the Old Testament could accurately be described as discipleship, such as Samuel to Eli, and Elisha to Elijah.