If a magazine editor asks you to write a profile of an up-and-coming novelist, she's asking you to write a biographical sketch, to give the readers a sense of the novelist as a person.
Profile comes from the Italian profilo, the thin colored border of cloth that outlines a garment. It came to mean any kind of sketch or outline, especially of faces. If someone compliments your profile means you look nice from the side (try outlining from other angles). If you have a criminal profile, your criminal record creates a picture of an active life of crime. A profile is also a drawing of the earth in cross-section, showing layers of crust.