Confirmation is a person’s public affirmation of their commitment to a life with Christ. If it follows infant baptism, it marks the point that the person is ready to confirm themselves the declarations made on their behalf by their parents and Godparents or Sponsors.
In the New Testament we read of the apostles and other church leaders laying their hands on a Christian’s head and praying for them to receive the gift of the Holy Spirit. This laying of hands is central to the confirmation service today. The person seeking confirmation renews the promises of their baptism, sometimes talks a bit about their faith journey so far, then the Bishop prays and lays his hands on them asking the Holy Spirit to fill them with strength to live their life as a Christian, before annointing them with oils. They then often receive holy communion for the first time.
If someone has not been baptised, they will normally be baptised and confirmed together, so the service combines both.