Baptism refers to a Christian ceremony that is done in different ways depending on the doctrinal belief of the particular church. Some do this by totally immersing the body into the water, a sprinkling of water, or pouring water on the body three times, all in a ceremonial manner.
Baptism simply symbolizes that a believer is dead to his or her past sinful life, and now coming alive in Christ as a new creation. On the other hand, christening refers to a process whereby a newly born baby is named and welcomed into the church. It does not necessarily need water to be involved, like baptism.
Some Christian congregations also believe in what is called infant baptism or pedobaptism, whereby a baby can also be baptized, whereas an adult that just gets converted into the body of Christ can only be baptized and not christened. Many churches do not believe in pedobaptism; they set a minimum age for the baptism of the child instead, at his or her own will.