The primary consecration of the faithful, and that which is most represented by parish life in its celebration of the sacraments of baptism, confirmation and the Holy Eucharist, is that of the sacraments of initiation. As Lumen Gentium n.10 (cf also Apostolicam Actuositatem n.3 in particular reference to baptism and confirmation as the basis of the office of the lay person in the Church) teaches:
Christ the Lord, High Priest taken from among men, made the new people "a kingdom and priests to God the Father". The baptized, by regeneration and the anointing of the Holy Spirit, are consecrated as a spiritual house and a holy priesthood, in order that through all those works which are those of the Christian man they may offer spiritual sacrifices and proclaim the power of Him who has called them out of darkness into His marvelous light. Therefore all the disciples of Christ, persevering in prayer and praising God, should present themselves as a living sacrifice, holy and pleasing to God. Everywhere on earth they must bear witness to Christ and give an answer to those who seek an account of that hope of eternal life which is in them.We can suggest that this baptismal/confirmational consecration represents a seed that needs to grow throughout a subsequent living of the Christian life, and that it therefore requires a "more" in order to achieve its fruition. That "more" can be expressed, and is lived, in many different ways in the life of the Church; but what each of those ways has in common is that they are in some way a more specific manifesting or expressing of the consecration first received in baptism and confirmation. In the anecdote above, that particular specification of baptismal/confirmational consecration comes about through experience of the charism of an ecclesial movement. When Pope Francis, and his predecessors, speak of the need for a "personal, living relationship with Christ" they too are speaking of a greater specification of the original consecration of baptism and confirmation which do, indeed, themselves involve a relationship with Christ. Marian consecration is to be understood in this way, too, as is the "baptism in the Holy Spirit" of the Charismatic Renewal.
The consecration, as consecration, represented by the profession of the evangelical counsels is one manner, with a particular excellence, of this specific living of the consecration first received in baptism and confirmation. Speaking of religious life, Lumen Gentium n.44, says:
Indeed through Baptism a person dies to sin and is consecrated to God. However, in order that he may be capable of deriving more abundant fruit from this baptismal grace, he intends, by the profession of the evangelical counsels in the Church, to free himself from those obstacles, which might draw him away from the fervor of charity and the perfection of divine worship. By his profession of the evangelical counsels, then, he is more intimately consecrated to divine service.