Brutus accuses Cassius of having an "itching palm." What does it mean?

"Itching palm" is simply a slang term for being money-hungry. Brutus makes it clear what he means when he continues with the accusation.

Let me tell you, Cassius, you yourself
Are much condemned to have an itching palm.
To sell and mart your offices for gold
To undeservers.

Brutus did not realize that Cassius had such a greedy, petty, selfish nature until he became hopelessly involved in an ill-fated partnership with him. Brutus is an idealistic, reclusive, philosophic type of man. Cassius is a scheming, selfish, untrustworthy man. Brutus finds out what a miser he is linked with when he asks for some gold to pay his soldiers and Cassius sends back a message in which he refuses the request. People who form partnerships of any kind often do not find out about their partner's character until too late.

Cassius is a real miser. Shakespeare shows this in several places. For example, after their heated argument in the tent in Act IV, Scene 2, Brutus calls for a bowl of wine and says:

In this I bury all unkindness, Cassius.

Cassius acts in character as a miser when he replies:

My heart is thirsty for that noble pledge.
Fill, Lucius, till the wine o'erswell the cup.
I cannot drink too much of Brutus' love.

He cannot drink too much of Brutus' wine, either, as long as Brutus is paying for it. He knows Brutus serves much better wine than he does. This kind of behavior is a sure sign of a miser. They are always freeloaders and cheapskates, penny-pinchers. They take as much as they can get and give as little back as possible. Earlier in the play, Cassius invites Casca to supper because he wants to sound him out about joining in the conspiracy which Cassius is trying to foment against Caesar.

CASSIUS: Will you sup with me tonight, Casca?

CASCA: No, I am promised forth.

CASSIUS: Will you dine with me tomorrow?

CASCA: Ay, if I be alive, and your mind hold, and your dinner
worth the eating.

A supper would not cost Cassius much. He would serve some bread and cheese, a few grapes and a little wine. Casca obviously dislikes Cassius. He has known him all his life and has been to his home before. He knows what kind of grudging hospitality to expect. He probably has no previous engagement but is simply telling a white lie. But Cassius persists. He raises the ante, so to speak, and invites Casca to dinner. This is evidently the main meal of the day, eaten in the afternoon, and would be more costly to provide. Casca sees that he won't be able to keep declining the persistent invitations, so he responds rudely. When he says, "...and your dinner worth the eating," he really means it. He doesn't expect much from Cassius, but he knows Cassius will expect a lot from him!

People should learn to identify misers by their behavior and not become too friendly with them. They are like black holes. Everything goes in, nothing comes out. Cassius is only thinking about his own welfare when he dreams up his conspiracy. He is afraid of Caesar and suspects that Caesar might be thinking of having him "put to silence" if he becomes king. After Cassius and Brutus have had their long talk in Act 1, Scene 2, Cassius says to himself:

Caesar doth bear me hard, but he loves Brutus.
If I were Brutus now, and he were Cassius,
He should not humor me.

In other words, if Cassius could become one of Caesar's favorites he wouldn't really care whether Caesar became king or not. But Cassius could never become a favorite of Caesar. Cassius is a bad-tempered, unlikeable man. That is why he needs Brutus to act as the leader of the conspiracy he is trying to form. Everybody likes Brutus. He is everything Cassius is not. Shakespeare intentionally characterized these two men as opposites in order to differentiate them for the audience.