Dr. Richard Parker was a scientist at Oscorp Industries in the works with his colleague, Dr. Curt Connors. Parker and his wife, Mary, were parents to Peter Parker. When Peter was only four years old, his parents disappeared and left randomly. They left Peter under the watch of his brother and sister-in-law, Ben and May.
Since his parents' disappearance, Peter has been trying to find the truth about who they are and where they went. Soon, Peter realized that his parents died in a plane crash. He then went to Connors to find more about the truth of his parents, but even Richard's closest friend and workmate did not know.
Richard Parker worked with cross-species spiders at Oscorp, unknown to many, Richard used his own DNA in his work so that only his bloodline could fully access and continue his work.
Way before the events of the film, Richard Parker was getting ready to leave New York, along with his wife. He dropped Peter off to his aunt's and uncle's house, saying his goodbye to him. He and Mary are no longer seen after this, as it remains unknown what happened to them, or where they are.
Much more is shown and told about Richard Parker's origin. It is revealed that Richard Parker has been friends of Norman Osborn for quite awhile, and that he was the one who created the Araneus Oscorpeus. Norman wanted Richard to use these spiders to create biological weapons, however, he refused to do so, then he quit his job at Oscorp, and fled the country. Afterwards, Norman framed him saying that he betrayed his best friend for the money that would be offered for his research. What Oscorp didn't know that Richard injected his blood DNA into the genetically modified spiders, so that it was only vulnerable to his bloodline, thus putting this plan on a hiatus. After Richard left his son with his aunt and uncle, he went into an airplane with his wife, only to be attacked by a man who was sent to kill him. Before Richard died, he managed to send a video message he recorded a while back, explaining about his experiments at Oscorp before his disappearance. The plane later crashes, killing Richard Parker. But Richard revealed to Peter that he's alive.
In a deleted scene, Peter is at Gwen's grave. The seasons flash by, and in winter a man standing behind him calls his name. The man reveals himself to be Richard Parker, visibly aged. Peter gets angry, believing his father to be dead. Richard tries to explain, but Peter grabs him by the collar and asks him where he's been. Richard explains the only way to protect him was to leave Oscorp, and Peter responds by hugging him and crying. Later, they walk along the cemetery and discuss why Richard came back. Richard then reveals to Peter that he's been aware of his identity as Spider-Man, due to his work with the cross-species spiders and that as his only living bloodline, Peter is the only one who could become a cross-species. He tells his son of his belief that he is destined to save the world and tells him Uncle Ben's famous words, "With great power comes great responsibility".