Original: Bartolo, still irked at Figaro for having facilitated the union of the Count and Rosina (in The Barber of Seville), promises, in comical lawyer-speak, to help Marcellina (aria: La vendetta — "Vengeance").
Simplified: Bartolo, still annoyed with Figaro for having made it easy for the Count and Rosina to marry (this had happened in Beaumarchais’ play The Barber of Seville), promises to help Marcellina.