Webster's defines "dissemble" as "to put on a false appearance: conceal facts, intentions, or feelings under some pretense."
In Shakespeare's depiction of him, Richard III is the very image of someone who dissembles. He shows sympathy when his brother George is led off to prison, but Richard is responsible for his imprisonment. Like Caesar, Richard pretends not to want the crown when it is really what he wants. He persuades Anne Neville to marry him, but at the same time he is trying to win the queen over to the idea of his marrying her daughter--his niece. In the eNotes analysis of his character, it is noted that "while Richard has no qualms about expressing his evil intentions in the starkest terms, it is his ability to persuade and deceive, his charming (even charismatic) guile, that comes to the fore and is his preferred mode of action before he is secured on England's throne."
Ironically, many scholars would say that Shakespeare instead of Richard III does the dissembling in this play. Richard III did not have a withered arm; he and Anne Neville had a loving relationship; he idolized his brother Edward; and it has never been confirmed that he killed the princes in the tower. The Richard III Society is dedicated to redeeming the reputation of this much maligned king.
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Some of the examples you can give in context to this theme: (I'm assuming you'll be able to build on them yourself)
1. The most obviously point lies in Richard himself. The only two consistencies in his character lie in his evil ambition and his continuously changing and dissembling nature
2. All the other characters dissemble too to an extent. They all pretend to be innocent (to a great degree, they actually believe they are innocent) when actually they have all participated in the War of Roses and so all of them have blood on their hands.
3. To some extent, dissembling also plays a role in defeating Richard, which is quite ironic. Richard reaches his height of power by dissembling and then falls because of the same tactic. Some of the men who pretend tI be on Richard's side are actually staunch supporters of Richmond, eg) Stanley.