Believer's baptism is the practice of baptizing only those people who have made a public and conscious profession of the Christian faith. Usually, this baptism is by immersion. This would stand in opposition to the idea that children can be baptized.
Believers baptism is clearly taught in Scripture as is evidenced by Jesus, the apostles, and many others. In particular, the Book of Acts records many such baptisms. Infant baptism is not explicitly found in the New Testament.