I would have him nine years a-killing. A fine woman! A fair woman! A sweet woman!
Nay, you must forget that.
Ay, let her rot and perish and be damned tonight, for she shall not live. No, my heart is turned to stone. I strike it and it hurts my hand. Oh, the world hath not a sweeter creature, she might lie by an emperor’s side and command him tasks.
If you are so fond over her iniquity, give her patent to offend, for if it touch not you it comes near nobody.
I will chop her into messes! Cuckold me?
Here Othello is talking to Iago about how he has a indescribable need to kill Cassio where he stands. For he saw Cassio with the Handkerchief that Desdemona had given Othello as a present.
Don’t do it with poison. Strangle her in her bed, the same bed she’s contaminated.
Get me some poison, Iago, this night. I’ll not expostulate with her, lest her body and beauty unprovide my mind again—This night, Iago!
Othello is dumbfounded that Desdemona would cheat on him so, so here he is saying that she should die for manipulating and playing with his heart.
And for Cassio, let me be his undertaker. You shall hear more by midnight.
Good, good, the justice of it pleases! Very good!
Iago is saying if you love her and she loves you then just let her cheat everything should be fine. Whereas Othello is just blinded by rage just wanting to kill her.
In this Othello and Iago are planning on how Othello is going to kill Desdemona, each of the them suggesting sinister things
Othello is pleased with the idea. Which leads Iago into saying that he wants to kill Cassio. Othello having no problem with Iago killing the man that is "cheating" with his wife gladly agrees. This might open a position for Iago to be promoted.
This scene allows Iago to kill Cassio while also throwing Othello's world all upside down. Also Iago made Othello think that this was all his idea. This is what leads into Otello killing Desdemona