The reason that Cinna says this (in Act III, Scene 1) is that he is giving the conspirators' major argument for why they thought it was necessary to kill Caesar.
The conspirators had decided that Caesar had been gaining too much power. They thought he was too popular among the people and they thought the people were going to make Caesar the king. If Caesar became king, the conspirators thought, Rome would not be a free republic as it had been.
So by saying this, Cinna is trying to justify what they have done -- he is claiming that they have saved Rome's freedom and liberty and have killed a tyrant.
These words occurs in in Act III, Scene 1 of Shakespeare's great play, Julius Caesar.
The meaning of the words, "Liberty! Freedom! Tyranny is dead!" are due to the belief that Julius Caesar was aiming for kingship.
A bit of historical context is important here. In 509 BC the Romans started a Republic by expelling the last king, Tarquinius Superbus. The Romans created a system of checks and balances, so that there would never be a king again. Power was diffused among Roman magistrates, and these magistrates were always collegial.
When Caesar grew in power, some believed that he took on too much power. For example, he was not only pontifex maximus (the highest priest), but also consul (Rome's highest position), and dictator for life. The last title was supposed to be used only for times of emergency and given up after the time had passed. So, the very fact that Caesar was dictator for life was shunned.
In light of these points, the conspirators really believed, even Brutus, that Caesar was leaving the Republic and starting something akin to a tyranny. So, when the conspirators killed him, they thought they were really fighting for freedom.