This line is delivered from Petruchio to Kate at Kate's house. Petruchio is claiming that Kate has won his love because she loved him so much and that she declared her love through oaths and kisses. This is both verbal and situational irony since Kate (also called "Kate the Cursed" in the play) is not a loving, affectionate being at first. She is belligerent, hateful, and violent to her sister (because she is jealous of Bianca) and to Petruchio (because Kate does not trust him to truly love her). Kate suspects Petruchio is only there to woo her for her father's money.
Later in the play, it turns out that Kate is the only true wife. She is loving and faithful to Petruchio and is the opposite of what she seems in the beginning of the play; this is also true of Bianca. While Bianca seems to be the perfect example of beauty, obedience and sweetness, she is conniving and hen-peckish as a wife.