The Greek word for "to forgive" (afiēmi) has many uses. It means "to let go, throw, hurl, cast, send forth...throw away, abandon, unburden...release...", just as a start. As an example of how this word and its related terms can be used, Mark has already used this word several times in what we have already read:
Mark 1:18 And right-away they let-go of the nets and followed him.
Mark 1:20 And right-away he called them, and letting-go of/abandoning their father, Zebedee in the boat with the hired-hands they went-way behind him.
Mark 1:31 And coming he raised her up by firmly taking her hand. Then the fever let-go-of her/released her and she began to serve them.
Mark 1:34 But he would not let-go/release the demons to speak, because they knew him.
A major emphasis in Jewish culture is the idea of release: release from debt, from sin, slavery, oppression, etc. This is probably a good approach to understanding a New Testament understanding of forgiveness.