This episode (Season 1, Episode 8) concludes the first major chapter of the family's rise.
Starts in 1429 with the death of Giovanni de' Medici.
Many deaths in the show/book (like Giovanni or Lorenzo the Elder) are dramatized; in reality, most died of natural causes.
Cosimo secures his power by convincing the Signoria to exile the Albizzi family rather than execute them—though the mercenaries have other plans.