"Whet" means to "sharpen by rubbing against as if a knife or to stimulate" according to Webster's Dictionary. By this definition, Brutus has been "sharpened or stimulated" against Caesar by Cassius. Cassius has been in Brutus' ear about all the bad things Caesar has done and what it might mean for the future of Rome if something is not done about it.
Since Cassius has begun all this talking, planting the seed of conspiracy and rebellion, Brutus can think of nothing else. The entire quote is:
Since Cassius first did whet me against Caesar, I have not slept. Between the acting of a dreadful thing and the first motion, all the interim is like a phantasma, or a hideous dream.
They have been in his ear, they have left letters for him to find, they have been after him to act on behalf of Rome against the tyrant who would enslave them all with his notions of government. This quote opens at the Ides of March dawns...little time is left for Brutus to make up his mind if he will act with or against the conspirators. He is under pressure, can not sleep, and is plagued with horrible visions of what will happen--either way he is tortured. The visions are not good no matter whose side he is on. Hallucinations and hideous dreams are no one's friend.
To understand the quote, it would probably be best to read it in its entirety:
"Since Cassius first did whet me against Caesar,
I have not slept.
Between the acting of a dreadful thing
And the first motion, all the interim is
Like a phantasma or a hideous dream.
The genius and the mortal instruments
Are then in council, and the state of man,
Like to a little kingdom, suffers then
The nature of an insurrection."
Brutus is considering the fact that ever since Cassius included him in the conspiracy to kill Caesar, he has not slept. He says that the waiting for something awful - "the interim" - is like an awful dream, and it is keeping him from sleeping at night.
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