Fleance is the son of Banquo. He escapes when the murderers hired by Macbeth kill his father in 3.3, thus making it possible for the prediction of the Weird Sisters (that Banquo's descendants will be kings) to come true. Fleance (and Banquo) are the ancestors of the man who became King James VI of Scotland and succeeded Queen Elizabeth on the throne of England to become King James I of England. The play Macbeth was probably performed in front of King James in 1606; at a time when Shakespeare's company had been named the King's Men.
Banquo (left, played by Ralph Michael) and his son Fleance (center, Paul Vieyra) take leave of Macbeth (Laurence Olivier, right), in Glen Byam Shaw's 1955 production at the Shakespeare Memorial Theatre at Stratford-upon-Avon.
Angus McBean, Harvard Theatre Collection