Most literary critics refer to Henry VI, Part 3 as a history play. In fact, it's the third installment in a series of Shakespearean history plays known as the "first tetralogy," which also includes Henry VI, Parts 1 and 2 and Richard III.
A history play is a genre that portrays English historical events that resonate with current political issues (current for Shakespeare's time), including matters of kingship, constitution, and rebellion.
If all this has you wanting to hit the snooze button, think again: Shakespeare spices up "history" with some good, old-fashioned fiction. He's the master of focusing on the good stuff and blowing it out of proportion for dramatic effect. In Henry VI, Part 3, Shakespeare took the best bits of English history during the Wars of the Roses, condensed it, omitted the boring stuff, and fictionalized entire interactions to create a political drama that can keep you on the edge of your seat.