A biographical sketch is an element of writing that uses the same things as a character sketch (description, narration, and exposition) to provide information about an interesting or relevant period in a fictional or non-fictional character's history. The effect often overlaps with that of a character sketch, in that the period described almost alwaays has some relevance in the development of the subject's character or personality. And now, an example!
Kilgore Trout was born in 1907 of American parents on the British island of Bermuda. Trout attended grammar school there until his father's job with the Royal Ornithological Society terminated. The family moved to Dayton, Ohio, where Trout graduated from Thomas Jefferson High School in 1924. Thereafter, he wandered around the country, workng at menial low-paying jobs and writing science-fiction in his spare time. His only known residences during, this period are Hyannis, Mass., Indianapolis, Ind., and Ilium and Cohoes, N.Y.
He has been married and divorced three times and has one child, Leo, a veteran of Vietnam.
As of 1974, Trout has written one hundred seventeen novels and two thousand short stories. Yet until recently he was little known. This regrettable situation is due to Trout's extreme reclusivity and his indifference to the publication of his stories. He was ill-advised in his choice of publishers, the chief one, World Classics Library, being a firm specializing pornographic novels and magazines. This ensured that his works would be distributed only to stores specializing in this genre. Yet Trout's work, with one exception, contained no explicitly erotic content. Without Trout's permission or knowledge, World Classics Library put lurid covers on his novels and used his short stories as fillers in "girlie" magazines.
from Kurt Vonnegut's Venus on the Half-Shell (1974)