Young Elizabeth's role is small but pretty significant. Elizabeth is the daughter of Queen Elizabeth and King Edward IV. She's also Richard's niece and the sister of the two young princes Richard has killed. Here's where things get creepy. After King Richard gets rid of his wife (Anne), he sets his sights on young Elizabeth, since he thinks their marriage will forge a nifty alliance between the two factions (4.4). Basically, Uncle Richard wants to use young Elizabeth as a pawn in his elaborate political scheme. (Gross.)
Thankfully this hook-up with Richard never actually happens. But Elizabeth does eventually become the wife of Richmond (a.k.a. King Henry VII), so she still gets used in a political game that's mostly controlled by men.
Young Elizabeth's marriage to Richmond/Henry VII is pretty significant because the union brings together the two warring households (the Lancasters and the Yorks) and puts an end to the Wars of the Roses (5.8.3). As Henry VII tells us, the marriage "will unite the white rose and the red" (5.8.3).