The vocation to Religious Life is truly a calling, a free gift of God, to enter into the inner circle of Jesus' companions. "Soon afterwards, he began going around from one city and village to another, proclaiming and preaching the kingdom of God. The twelve were with him, and also some women who had been healed of evil spirits and sicknesses." (Luke 8:1-3)
All Catholics are called to Holiness, but those in religious life (monks, nuns, friars, religious sisters) are called to a more literal following of the historical life of Christ. It is a call to live the Gospel: "The consecrated life truly constitutes a living memorial of Jesus' way of living and acting as the Incarnate Word in relation to the Father and in relation to the brethren." (VC)* All are called to live a certain poverty, chastity and obedience but the Religious is called to manifest the extreme poverty, chastity and obedience of Jesus. For example, the rich young man kept all the commandments, but when asked to relinquish all of his belongings and follow Jesus he went away sad. The vocation to religious life is essentially the same call.
The Desert Fathers (hermits) can be considered the first to enter religious life. Some say they did so because Christianity had gained greater acceptance and it was no longer likely that a person would suffer martyrdom in the literal sense. Therefore, they chose to leave the world and 'crucify' their own desires in order to die to self in a spiritual martyrdom. The religious life is a white martyrdom, through which the individual is emptied of self and filled with Christ. This can also be seen as the path of contemplative union with God.
St. Bernard and St. Thomas Aquinas referred to Religious Life as a second baptism. As in the first baptism we die to our previous life of sin, in professing perpetual vows we die to our life in the world. We are consecrated, or set apart, for the service of God. (This is one of the reasons why the Religious Sister receives a new name, because she has died to her previous life. It also indicates a new kind of relationship with God, like when Abram was renamed Abraham.) This requires a complete giving of self, a pouring out, that is modeled by Jesus' death on the cross and the outpouring of blood and water from his sacred side. "Greater love has no one than this, that he lay down his life for his friends." In this way, the religious life is a life of sacrifice for love of neighbor and, ultimately, for the salvation of souls.
*Post-synodal Apostolic Exhortation, Vita Consecrata (Consecrated Life) by Pope St. John Paul I