Cassius's letters to Brutus are all aimed to manipulate him into joining the conspiracy to kill Caesar. Note, first of all, that they are all forgeries. At the end of act 1, scene 2, Cassius describes his plan to write multiple letters, pretending that they have been written by different Roman citizens. (Note also that Cassius even goes so far as to alter his handwriting to further the illusion.)

One of the critical passages, as Cassius outlines his plan in act 1, scene 2, can be found when Cassius states, in reference to Brutus himself:

Writings, all tending to the great opinion

That Rome holds of his name

Historically, Rome began as a monarchy before transitioning into a Republic. As legend had it, one of the critical leaders in driving out the last of these kings and instituting the Republic was Brutus's ancestor, Lucius Junius Brutus. In this respect, Brutus's entire family legacy is closely intertwined with the Republic itself, a factor which Cassius exploits in the letters.

These letters are exhortations to action, giving Brutus the impression that Rome is under threat of falling under the domination of Caesar, requiring Brutus to act decisively to prevent this from happening. Brutus himself invokes the comparison with his own ancestry, and his family's role in overthrowing the monarchy, stating:

Shall Rome stand under one man's awe? What Rome?

My ancestors did from the streets of Rome

The Tarquin drive, when he was call'd a king (act 2, scene 1).

In this respect, we can see the impact that these letters have had on him and the way in which they bring him to recall his own family legacy and its history in ending the monarchy and creating the Republic. Just as his ancestors had safeguarded Rome against Tarquin, now Brutus is being exhorted to do the same against Caesar.

Cassius wrote many fictitious letters and sent them to Brutus in a number of different ways. Shakespeare could not reveal the contents of all the different letters because (1) it would have been redundant, and (2) he didn't have enough space. We can deduce the general contents of the letters from what Cassius says about them right after he and Brutus end their conversation in Act 1, Scene 2, as well as from the one letter which Brutus is handed by his servant Lucius and which he reads partially aloud in Act 2, Scene 1. 

After Brutus and Cassius separate in Act 1, Scene 2, Cassius tells the audience in a soliloquy what he intends to put into the letters he plans to write to Brutus.

I will this night,
In several hands, in at his windows throw,
As if they came from several citizens,
Writings, all tending to the great opinion
That Rome holds of his name, wherein obscurely
Caesar's ambition shall be glanced at.
And after this let Caesar seat him sure;
For we will shake him, or worse days endure.

Then that evening, in Act 2, Scene 1, Brutus is given a letter by Lucius which the boy says he found in the window. Brutus reads parts of the letter aloud to himself. The contents appear to be along the lines that Cassius had said he would put in all his forged letters.

“Brutus, thou sleep'st: awake and see thyself!
Shall Rome, &c. Speak, strike, redress!”
“Brutus, thou sleep'st: awake!”
Such instigations have been often dropp'd
Where I have took them up.
“Shall Rome, &c.” Thus must I piece it out.
Shall Rome stand under one man's awe? What, Rome?
My ancestors did from the streets of Rome
The Tarquin drive, when he was call'd a king.
“Speak, strike, redress!” Am I entreated
To speak and strike? O Rome, I make thee promise,
If the redress will follow, thou receivest
Thy full petition at the hand of Brutus!

The audience will understand that the citizens of Rome are calling upon Brutus to stop Julius Caesar from his obvious attempt to take over complete power in Rome. As Cassius said to himself in Act 1, Scene 2, the letters all tend to the great opinion Rome has of his famous name and all hint at the threat posed by Caesar's ambition. Brutus shows himself easy to manipulate when people appeal to his distinguished family reputation and his personal honor. He is an example of a man who is so honest that he does not suspect others of being dishonest. In King Lear the villainous Edmund finds it easy to manipulate both his father the Earl of Gloucester and his brother Edgar because both are so honest that they do not detect duplicity in others. In Act 1, Scene 2 of King Lear, Edmund says to himself:

A credulous father! and a brother noble,
Whose nature is so far from doing harms
That he suspects none: on whose foolish honesty
My practices ride easy!

The letters that Brutus receives, all of them written by Cassius, are very important in the play because they persuade Brutus to join the conspiracy to assassinate Julius Caesar. They were important historically, too, because without Cassius' idea of writing all those letters Brutus might not have joined. And without Brutus the plot might never have succeeded. Cassius could get Romans to join in his plot against Caesar because he could tell them that the distinguished Brutus was taking the lead.