Othello hearing the screams from Roderigo thinks that Iago has killed Cassio. Cassio is only injured and this cues Othello to kill Desdemona.
Ay, 'twas he told me on her first. An honest man he is...
To not cause suspicion from Cassio and Iago not trusting Roderigo in case he reveals his plan, he kills Roderigo out of spite. Iago never cared for Roderigo.
She give it Cassio? No, alas, I found it, and I give't my husband.
Filth, thou liest!
Othello about to kill Desdemona tells her there is no coming back from this and that it too late. While a worried Desdemona tries to reason with him he then strangles her. This is the tragedy of the play. Iago has convinced Othello to do this.
I kissed thee ere I killed thee. No way but this, killing myself, to die upo a kiss.
All that is spoke is marred.
O bloody period!
Othello explains his reason to why he killed Desdemona, saying Iago was the one who claimed that she was cheating on him. Emilia is putting the pieces together, ready to expose Iago's truth.
Emilia reveals that she gave Iago the handkerchief, and that he used it to put it into Cassio's possession. Revealing the truth and evidence that Othello kept coming back to.
Othello, knowing that if he stayed alive would be held prisoner and overwhelmed with what he has done, kills himself. Marking the last death of the play. It is unknown if his death would satisfy Iago.