Becoming a member of the Body of Christ - the Church 

Baptism is the first of the seven sacraments of the Catholic Church, and it marks the beginning of a person’s journey in to faith with God. It is one of the three Sacraments of Initiation.  In some denominations this Sacrament is referred to as Christening.  Literally making Christ-like.
Through Baptism we become members of Christ, and we are welcomed into the Church.
They now share in the rights and responsibilities of the Church. 

It is traditional in the Roman Catholic Church that parents bring their children to Baptism. The parents participate in a formation programme (aka Baptism Preparation Course) so that they understand their role as the 'first educators of faith'.
Bringing a child forward for baptism is a wonderful gift a family bestows on a child.  It also brings responsibility for supporting the child in their journey of faith and explained in this document: Information for families bringing infants forward for baptism.
Families are helped in this responsibility by the child's godparent/s.  Only one is required and they have to meet certain requirements in order to ensure they can carry out their responsibilities.  They have a particular role as Godparent.

Other relevant topics:
Click here to find out more about infant baptism and why it is done.
** source; Auckland Diocese**