Macbeth Act III, Scene i Summary

At Macbeth's new palace in Forres, Banquo, alone on stage, delivers a soliloquy (a speech that reveals his innermost thoughts to the audience), announces that Macbeth is totally suspect – it's likely he played dirty to get the crown. (Remember, Banquo was present when the witches' prophesized that Macbeth would be king. The witches also said that Banquo's descendents would be kings as well.)
Short of being horrified by Macbeth's act, he takes some time to note that this must mean his part of the prophecy, regarding his royal seed, will also come true.
Banquo pipes down when the newly crowned Macbeth, his lovely Queen, and a posse of noblemen enter the room. (Macbeth is looking rather cozy wearing his new crown and hanging out in his new digs.)
Macbeth speaks very sweetly to Banquo, calling him his honored guest and requesting his presence at a fancy banquet to be held that night.
Banquo plays it cool and ever so casually says that he's sorry, but he has other plans. Then Macbeth ever so casually asks what Banquo will be up to, and finds out that he'll be riding off somewhere before dinner.
Having obtained the information he needs, Macbeth changes the subject to the fact that the "bloody" Malcolm and Donalbain are suspiciously missing, and respectively hiding out with new friends in Ireland and England. Plus, it seems that Duncan's sons are busy "not confessing" to Duncan's murder – instead, they're spreading nasty rumors about their father's death.
Macbeth adds a little "by the way" as Banquo leaves, asking if his son, Fleance, will be riding along with him that evening. Fleance will indeed be going, and upon hearing this, Macbeth bids them farewell.
Everyone except for Macbeth and some servants leave the room.
Macbeth then has a servant call in the men he has waiting at the gate.
Left to himself, Macbeth launches into a long speech about why it's necessary and good to kill his friend, Banquo. Macbeth fears Banquo's noble nature, wisdom, and valor. Plus, if the rest of the witches' prophecy comes true, Macbeth notes he will have sold his soul to the devil (by killing Duncan) for Banquo's kids to take his crown.
He concludes his speech by inviting fate to wrestle with him, and says he won't give up until he's won or dead. (Gosh. It seems like it's getting a whole lot easier for Macbeth to think about murder, don't you think? It is interesting to compare Macbeth's attitude towards murder here to what he was thinking at the beginning of the play.)
The two men at the gate are brought in, and we discover that Macbeth intends for them to murder Banquo and his son while on their ride. Macbeth gives speeches to the two murderers about how Banquo is their enemy and anything bad that has ever happened to them is surely Banquo's fault.
Macbeth says that no turn-the-other-cheek Christianity is necessary here.
The murderers respond by saying that they are only "men," and then Macbeth uses the technique he learned while being berated by his own wife: he claims they're not real men if they're not brave enough to murder a man for their own good. (Seriously. It sounds like he's channeling his wife here.)
The henchmen point out that such speeches are lost on them, as their lives are pretty crappy anyway. They're fine with taking a chance on eternal damnation.
Macbeth notes that Banquo is his enemy, too, and he'd do the kingly thing and just have him publicly killed, except that they have a lot of mutual friends, which might make things a little awkward.
The murderers agree to kill Banquo, after which Macbeth throws in that they'll have to kill the boy Fleance, too. He'll let them know within the hour about where to find Banquo, but right now he has to go get ready for a dinner party.

Act III, Scene ii

Act II, Scene iv