Who is Thirty Tyrants from The Last Days of Socrates and what is their importance?

The Thirty tyrants are important to the context of Socrates' trial and execution. In 404 BC Athens Surrendered to Sparta in the Pleoponesian war. As victors, Sparta installed a Spartan style government, an oligarchy, which is rule by a select few arristocrats. In the case of Athens, thirty tyranical leaders.

The significance to Socrates is that a number of these tyrants were former pupils of his, such as Critias. Socrates gives an example of himself standing up for justice in the apology. The tyrants ordered him to arrest Leon of Salamis, simply because the state wanted his money. Socrates flatly refused. He didn't get a chance to be punnished for this because the oligarchy collapsed in 403 BC and was replaced by democracy.

There was an armistice, a legal agreement that no one could be tried for political crimes from before the reinstallment of democracy. Nevertheless, Athens wanted a scapegoat for the tyranny and Socrates was their choice. His official charges are worshipping gods of his own invention and corrupting the minds of the youth. These are vague and fake.

You may be asked why Socrates is on trial. The Thirty Tyrants is the real reason why. Basically Socrates taught some nasty people whom Athens hates.