Discipleship is the practice by which someone is followed and
their doctrine is spread. Assuming you are asking this in a
biblical context, discipleship is the practice of following Jesus,
and thus encouraging others to follow him as well. It is the way by
which his teachings and his doctrine are spread to the world. More
specifically, being a disciple is about holding to Jesus'
teachings, and falls synonymous to the word 'discipline'.
Christians were first called Christians because the disciples were
like Christ.