What does Brutus mean when he says that he is at war with himself in Act 1, scene 2 of Julius Caesar?

Brutus says this in reply to a remark made to him by Cassius in Act scene 2. Cassius has commented that he has noticed that Brutus has adopted a stern and troubled look lately. He does not look upon him with the favourable and affectionate expression that he has become accustomed to. Brutus then says the following:

Cassius,
Be not deceived: if I have veil'd my look,
I turn the trouble of my countenance
Merely upon myself. Vexed I am
Of late with passions of some difference,
Conceptions only proper to myself,
Which give some soil perhaps to my behaviors;
But let not therefore my good friends be grieved--
Among which number, Cassius, be you one--
Nor construe any further my neglect,
Than that poor Brutus, with himself at war,
Forgets the shows of love to other men.

In this extract, Brutus tells Cassius that he should not be misled if he seems to be hiding his true feelings. The image that he projects is only because he is troubled within himself. He has been disturbed by inner turmoil in his mind which may have tarnished his behaviour. He tells him that his close friends, amongst whom he includes Cassius, should not be concerned too much, nor interpret anything from his offhanded behaviour, because it is just a reflection of the fact that he is fighting an inner battle with himself and therefore neglects to show any courtesy or love to others.  

The fact that Brutus expresses an inner turmoil gives Cassius the ideal opportunity to prey on Brutus' uncertainty. He has already formulated a plot to get rid of Caesar, whom he despises and is jealous of, and Brutus would be the perfect candidate to join his malevolent band of conspirators since he is a man of honour and a trusted confidant of Caesar's. 

It becomes clear, later, that Brutus fears Caesar attaining greater power and authority by being elected emperor and this seems to be what has been troubling him so much. When he and Cassius hear a flourish and shouting, he asks:

What means this shouting? I do fear, the people
Choose Caesar for their king.

Cassius immediately asks him if he fears the fact that Caesar is being offered the crown because, if it should be so, it also means that he does not want it to happen. To this, Brutus replies:

I would not, Cassius; yet I love him well.

Brutus then asks Cassius why he is holding him back. If he has something to say, he has to do so quickly as long as it is for the good of Rome. He states that if he should be faced with death and honour, he would easily choose the latter for he has greater respect therefor and does not fear death. 

The sly Cassius sees Brutus' remarks as an opportunity to ensnare him in his plot. He gives a long speech and consistently flatters Brutus, and eventually, by repeatedly stressing the fact that Caesar is weak, frail, inept and a danger to the common good, persuades him to meet with him to discuss the matter further. At the end of their talk, Brutus says:

...For this time I will leave you:
To-morrow, if you please to speak with me,
I will come home to you; or, if you will,
Come home to me, and I will wait for you.

The seed for Caesar's murder has been firmly planted.