It is worth noting the context in which Othello must give explanation for Desdemona's affections. He is a very high ranking military figure, sort of a foreign celebrity in Venice ( he reminds me in some ways of Lafayette's popularity in the US after the Revolutionary War), wined and dined in the best of homes as an honored guest, including the home Desdemona and Brabantio.
All this notoriety is worth noting, because, Othello is accused before the Duke of Venice by Brabantio (his former welcoming host) of bewitching Desdemona so that she is made to act against her will and love and marry Othello. Brabantio says:
I therefore vouch again,
That with some mixtures powerful o'er the blood,
Or with some dram conjured to this effect,
He wrought upon her.
Against which charge Othello, this amazing celebrity, must defend himself. Beginning with the words:
[A]s truly as to heaven
I do confess the vices of my blood,
So justly to your grave ears I'll present
How I did thrive in this fair lady's love
And she in mine.
What follows is one of the most oft quoted speeches in Shakespeare's canon (I, iii, lines 128-169), in which Othello describes (as mentioned in the previous answer) how he wooed Desdemona ending with the words: "This only is the witchcraft I have used."
Othello believes that Desdemona has affection for him because she pities him. Othello is questioned by Brabantio, the Duke, and the senators when Brabantio finds out that Desdemona has wed Othello. Othello is called to court where he reveals the history between him and Desdemona. When the two met, Othello told Desdemona about his life journeys and his upbringing. Desdemona wanted so much to hear about Othello's life that she returned to him to hear more of his story. After Othello finished his story, Desdemona told him that if he had a friend with a similar story, then she would be wooed by his words. Othello took Desdemona's hint and tells his audience, "Upon this hint I spake: She lov'd me for the dangers that I had pass'd, and I lov'd her that she did pity them" (I.iii.166-168).