DNA replication is a process where DNA makes a copy of itself. It must happen before mitosis (which is when a cell divides) so that each new cell created contains the same amount of DNA as the original cell. DNA replication also happens before meiosis, which is the process of producing gametes (also known as sex cells, such as sperm or egg).
Transcription is the process of making a copy of a portion of one strand of DNA. This copy is then sent to the ribosomes of a cell, where it is used to make a protein in the process of translation. Protein synthesis refers to the steps required to use the DNA code to correctly make a protein.