Cecil Frances Alexander (1818-95) is the composer of this extremely popular hymn, There Is a Green Hill Far Away.
It draws its inspiration from the Apostles Creed especially the line that goes, ‘Suffered under Pontius Pilate, was crucified, dead, and buried.’
It is believed to have been written at the bedside of a sick young person. The writer gives substance and answer to those who inquire why Jesus died. She talks about God’s forgiveness.
She speaks of how man can reclaim his original close relationship with God and suggests the only possible response is the total giving of loving self. The event was for us.
Cecil Frances Alexander, besides being a hymn writer, was also a poet and was born in Dublin to Major John Humphreys and his wife Elizabeth (nee Reed).
Source: ChristianMusicandHymns.com
Here's more on the Biblical basis for the words... The reason why Janet told Peter, belief in the words of the hymn means certainty of salvation.
Even though the hymn was written with children in mind, her clear presentation of the redemptive work of Christ has allowed the hymn to prosper and continue to find favor even among adults.
In the first stanza, the green hill is Golgotha (Calvary), far away in both time and geography. According to lore, Alexander would often pass by a green hill between her home and Derry, and she associated it with what Calvary might look like.
The second line, “Without a city wall,” most likely was intended to mean “Outside a city wall,” and some hymnals make that change. The last line, “Who died to save us all,” is borne out of Scriptures such as 1 John 2:2 (“he is the propitiation for our sins: and not for ours only, but also for the sins of the whole world,” KJV) and Isaiah 53:6 (“the Lord hath laid on him the iniquity of us all”).
Similarly, the second stanza speaks of a substitutionary atonement, as in Galatians 3:13 (“being made a curse for us”), Isaiah 53:5 (“he was wounded for our transgressions, he was bruised for our iniquities”), or 2 Corinthians 5:21 (“For our sake, he made him to be sin who knew no sin,” ESV).
The third stanza speaks of a forgiving act, as in Hebrews 9:22 (“without the shedding of blood there is no forgiveness of sins,” ESV) or Ephesians 1:6–7 (“To the praise of the glory of his grace, . . . In whom we have redemption through his blood, the forgiveness of sins,” KJV; also Colossians 1:14). This act also makes us better, bringing about change (2 Cor. 5:17, “Therefore if any man be in Christ, he is a new creature,” etc.). As one commentator noted, “We are saved to be sanctified. Jesus wants to make us good women: good sisters, good wives, good mothers, good neighbors, good friends. He died to make us good.”[5] Lastly, the third stanza frames the cross as a gateway to heaven. Jesus himself said, “I am the door. If anyone enters by me, he will be saved and will go in and out and find pasture” (John 10:9, ESV).
Read the full story behind this hymn here