In act four, Richard has changed a bit. For starters, by the end he is no longer king. He has given up that title. He is resigned. He is truly and completely broken, while Henry is just a jerk, or at least looks it. He takes the crown after treating himself as practically a king anyway. (I loved the beginning where everyone and anyone was throwing down their gage.) And then after taking the crown, he and his men make Richard read a list of his wrongs publicly. Harsh! I didn't really understand the part with the mirror, but I guess it also shows how upset Richard is. "Fair cousin? I am greater than a king." Richard is is the process of accepting who he now is. I have a feeling that acceptance won't come. Henry's feelings and person, however, are harder to pin down in this act. He doesn't talk much, and when he does, he seems indifferent, sometimes sad, sometimes smug. It's hard to tell.
As far as what they do, I'm going to keep it simple. Richard gives up the crown and Henry takes it for his own. It's a trade, unwilling but done. One had what the other wanted and so paid for it.
And what does it mean? Again, simply it means that England has a new King and that is Henry. It means that Richard isn't going to be welcome in England much longer. It means that things are changing and are going to change. I liked this act. Very readable and added a lot to the story.