The quote you have given is of course a paraphrase of the original Shakesperian English. In Act II scene 1, Iago observes that Cassio takes Desdemona's hand to lead her away and talk to her about his situation. He plans to use this as evidence against him in his plot to gain his revenge against Othello. As the other characters exit, and Iago is left with Roderigo, Iago tells Roderigo that Desdemona will soon tire of Othello, but the man she will most likely go to will be Cassio, and cites what he saw as proof of this:
Didst thou not see her paddle with the palm of his hand? Didst not mark that?
In response to this manipulation and temptation from Iago, Roderigo argues that this was just politeness, or "courtesy," on the part of Desdemona and not indicative of any other feelings.