Brutus is the main character and tragic hero of the play. It is through his character that the themes of the play are expressed. Through his soliloquies, Brutus shares his thoughts and feelings with the audience. We understand the conflicts within him. For example, the soliloquy which opens Act II shows how Brutus tries to justify Caesar's assassination by saying it would be for the good of Rome, not because Brutus has anything against Caesar. This gives us insight into Brutus' misguided sense of duty to Rome and his feeling that if Caesar is allowed to live, Romans will lose their freedom. Brutus is idealistic in his political beliefs and views the assassination as an honorable, necessary act. It is through his soliloquies that the audience understands the issues of Brutus' character.
Concerning Shakespeare's Julius Caesar, you should state which speeches you mean to get a more specific answer, but I'll take one soliloquy for you.
In Act II:i Brutus is left alone after he asks Lucius to bring him a taper, or candle, beginning in line ten. He then speaks at length as he attempts to reason out what the future might hold for Caesar and for Rome. Brutus is trying to figure out how ambitious Caesar is, and whether or not Caesar is planning on accepting the crown and becoming emperor of Rome.
This speech emphasizes the question of whether or not Caesar needs to be stopped; reveals Brutus as a character who likes to thoroughly think things through; also reveals Brutus as a character who may be overreacting; and therefore reveals Brutus as a character who may be too pliable, too easily influenced, when it comes to the opinions of others.
These all enhance the meaning of the tragedy in the ways I've mentioned. This siloliquy furthers the plot and foreshadows the tragic downfall.