In Act IV, he crumbles. Othello discusses his race throughout the play—usually in response to something a white Venetian says—but here he makes his first negative reference to it, suggesting that perhaps his Blackness is to blame for his lack of conversational ability. It is a quiet moment, but a hugely significant one. It marks a turning point: Othello has fallen victim to the same racist logic (or illogic) that rules the thinking of people such as Iago and Roderigo. Like those men, Othello wants to place the blame for his feelings of inferiority somewhere and winds up laying that blame not where it belongs (in this case, at Iago’s feet), but on his own skin. The floodgates have opened, and now Othello is in danger of believing all of Iago’s racist nonsense. In the next lines, Othello compares himself to a toad living in a dungeon, as if he has begun to suspect that his Blackness makes him a loathsome animal, somehow less than human.
When Othello feels his wife's supposed sexual infidelity has soiled his good reputation, he compares his once good name to his "begrimed and black" face. In other words, Othello associates the blackness of his own skin with something dirty and stained, which is exactly the kind of thing that the racist Venetian characters (like Brabantio) have been saying all along.
By this moment in the play, Othello seems to have internalized the racist ideologies of other characters. He sees himself as a soiled (and soiling) black man.
Some versions of the play read "Her name, that was as fresh / as Dian's visage is now begrimed and black / as my own face." This substitution may oppose the idea that Othello is buying into the racist insults.