Biff's babysitter watched Biff Tannen when his parents, Kid Tannen and Myra Benson got married in Hill Valley, California on December 6, 1936, at the Church of the Heather. The marriage was simply for the purpose of making it seem like Biff Tannen, who was born earlier that year, wasn't born out of wedlock. The two parted ways immediately after the wedding, and neither parent wanted Biff. Because of this, Kid's mother, Gertrude Tannen, took custody of him. Before he left his son, Kid gave Gertrude a forged birth certificate that stated that Biff was born on March 28, 1937.
In an alternate timeline where Biff Tannen brought a an almanac from 2015 to 1955 to make himself rich, Dr. Emmett Brown used his time travel chamber to travel from 1983 to 1936 to stop the wedding. He had hoped that stopping the wedding would prevent Biff from being born, but upon hearing a crying baby in the church, Doc realized that Biff had already been born.
The babysitter offered to give Biff to Doc since his parents didn't want him. However, Gertrude refused since she was his family. Thus, Doc planned to come up with a "Plan C" once he arrived in 1983, and disappeared into the future as he was looking at his pocketwatch. However, upon returning to 1983, he was caught by Biff and his gang.