Each of the Gospels, Matthew, Mark, Luke, and John, relate the life, work, and ministry of Jesus from their own perspective. However, Matthew, Mark, and Luke all look at the same set of events, and are given the name "Synoptic" (Syn=same, like synonym; Optic=eye). They all look at Jesus' birth, life, three year public ministry, his trial, execution, burial, and resurrection. John chooses a much smaller sub-set of events and expands them in much different way.
The Synoptic Gospels emphasize witnessing the events, retelling of the events happened, and presenting the facts and observations of those who were present. Peter says these were not "cleaver invented stories."
Those who travelled with Jesus told their story of "how it happened." They went preaching and teaching that Jesus was the promised Messiah, who was crucified and resurrected. They preached first in Jerusalem, and moved out in widening circles, Judea, Samaria, the Mediterranean, and the ancient world. They were preachers and teachers, so it hadn't occurred to them to write down what happened until thirty years after the resurrection two factors caused them to want a permanent record of the events.
In AD54 Nero became emperor of Rome and the persecution of Christians escalated. All of the Apostles would be martyred except John who was exiled. Second, most of the Apostles where hitting their mid-sixties, and were fast becoming aware of the shortness of life. Realizing the importance of their direct relating of the events, the Synoptic Gospels were written.
Matthew, the senior tax collector turned disciple and chosen an apostle, was a direct eyewitness. He was with Jesus the three years of His public ministry, present at the crucifixion and witness of the resurrected Jesus. Matthew was a Jew and he wrote to a Jewish audience. He expects his readers to understand his references to Jewish observances and practices.
Mark has a different background relating to the events and his place in the life of the first century Church. Mark was not an Apostle. He was not even a disciple who travelled with Jesus during His three year public ministry. Mark was a very young man during the time of that ministry. It appears he was not on his own, and perhaps as young as twelve or thirteen years old. However, he was with Jesus from time to time as his mother, Mary, was a disciple. And additionally, Mark's older cousin was Barnabas, the Apostle. He would travel with Paul and Barnabas on a Mission trip. Eventually Mark ends up in Rome with the Apostle Peter. So Mark had first hand and inner circle knowledge of the events, but not in their entirety. Mark would be writing at Rome, within a mixed community of Jewish and non-Jewish Christians.
Luke never met Jesus. He was a Gentile physician living somewhere between Antioch and Troas. He meets Paul on a Mission Trip, joins him, travels with him for 18 years until Paul's martyrdom in Rome. With an educated and scientific background, Luke sets forth an orderly account, a careful compiling of the testimony he gathered of not only Jesus, but of the spread of believers in the first decades of the Church (a separate book called The Acts of the Apostles). Luke writes his two volume account for an audience of one man, Theopholis.
The three Synoptic writers look at the same events; each brings their own history into the manner of the telling giving us three different perspectives on the events.