I'm assuming that the soliloquy you're referring to is actually at the end of Act 3, scene 1 ("O, pardon me, thou bleeding piece of flesh..." (3.1.255-277), as there is no soliloquy at the end of 3.2.
In his soliloquy, Marc Antony apologizes to Caesar's corpse for appearing to be civil toward the conspirators, and essentially vows to avenge Caesar's death. Antony predicts, among other things, a civil war so fierce that "mothers shall but smile when they behold/Their infants quartered with the hands of war" (3.1.269-270); he also suggests that Caesar's spirit will have a hand in this war of revenge.
Antony's soliloquy clearly foreshadows the action of Acts 4 and 5. By the end of Antony's funeral speech in Act 3, scene 2, the Romans have turned against the conspirators and are already seeking revenge for Caesar's murder. Brutus and Cassius are driven from the city and forced to gather support hastily in preparation for a war with Antony, Lepidus, and Octavius, and by the end of the play, the war that Antony foreshadowed has occurred. Similarly, Brutus is visited by Caesar's ghost, who tells Brutus, "Thou shalt see me at Philippi" (4.3.285)--the place where Brutus ultimately takes his own life.
At the end of Act III, Scene 2, Antony's speech is not a soliloquy because he speaks in front of people. Instead, this type of speech is called a monologue, a speech by one person before others. Like a soliloquy, a monologue expresses an individual's thoughts and feeling, but this expression is before an audience, not alone.
In this monologue, which comes after his powerful oration, Antony introduces the idea of mutiny by putting the idea out to the agitated plebeians, although he pretends that he believes that the conspirators have acted out of honorable intentions:
Good friends, sweet friends, let me not stir you up
To such a sudden flood of mutiny.... (3.2.202-204)
Further, Marc Antony pretends that he negates any kind of mutinous thoughts, but then he foments the crowd by creating a hypothetical situation, saying if he were Brutus and Brutus were he, there would be an Antony who would encourage retribution against the assassins, making even stones to rise up.
Would ruffle up your spirits, and put a tongue
In every wound of Caesar's that should move
The stones of Rome to rise and mutiny. (3.2.222-224)
This call to rise up and mutiny against Brutus and the other conspirators clearly foreshadows the civil war that soon begins.
This speech, which foreshadows the defeat and deaths of the conspirators, has several memorable lines.
Over thy wounds now do I prophesy,
Which like dumb mouths do ope their ruby lips
to beg the voice and utterance of my tongue.
Here, Antony creates a metaphor expressing the idea that Caesar’s wounds are mouths that are unable to speak, so Antony will speak for them. In so doing he has done a masterful job of convincing the Roman populace to turn against the conspirators.
Then Antony prophesy's what he believes will happen next:
And Caesar’s spirit ranging for revenge,
With Ate by his side come hot from hell,
Shall in these confines with a monarch’s voice
Cry, “Havoc,” and let slip the dogs of war.
Antony has used another metaphor, referring to the armies he shall command as as the “dogs of war.” This implies that the soldiers shall be merciless to the point of being animalistic in their violence.
Notice also that Antony refers to Caesar’s spirit has having a “monarch’s voice.” This is a special stab at the conspirators, whose fear of Caesar’s quest for dictatorial power is what spurred them to action in the first place. The implication is that Caesar will be even greater and more dangerous in death than he was in life.
This turn of events was not wholly unexpected by the conspirators. Cassius warned Brutus not to allow Antony to speak at Caesar’s funeral:
Know you how much the people may be moved
By that which he will utter?
Brutus makes several crucial decisions against the advice of Cassius. This was the one that turned the tide against them.