DARIUS

The time is early 5th century B.C. (Marathon 490 B.C.), i.e. as far as our Greeks are concerned. For more detail see "The Rise of Persia" page 156
Darius, king of Persia, forever greedy, extended his territory and took over the Greek colonies in Asia Minor (in presentday Turkey). They resented him and the tyrants he had imposed on them and finally rebelled. So he went to punish them. The mainland Greeks had the unfortunate idea of helping their compatriots across the sea and sent some ships. Not enough to really help their friends, who were crushed by Darius, but enough to make him very angry indeed. Darius thought the time ripe to subdue the whole of Greece and get some more tribute paid him. He miscalculated and his enormous army - which he had spent 10 years preparing - was destroyed by a Greek force far inferior in number, but superior in strategy and determination. He met his Waterloo, sorry that was Napoleon, his Marathon*, retreated back into his enormous empire to prepare a new army and a new invasion of Greece. But he died before he could make his promise of "I'll be back" come true.

* When the Greeks (mostly Athenians) had defeated the Persians at Marathon, they sent a messenger back to Athens with the good tidings. He ran all the way, arrived at Athens, told his news and then died of exhaustion. That's were the name of the "marathon" running contest comes from. And so as not to drop down dead upon arrival, we put in a lot of practice runs beforehand.

 

XERXES

Son and successor of Darius as king of the Persian Empire. He followed in his father's footsteps and tried to subdue those irritating little Greeks who just wouldn't bow to the superior Persian rule. He certainly didn't take kindly to a lack of subservience, cf. lesson 13, supplementary text p 166
ὁ Ξέρχης τὸν Ἑλλήσποντον διαβαίνει
where even the sea is taught a lesson for not serving the Great King as is his due.
He invaded Greece (remember lesson 14:
ἡ ἐν ταῖς Θερμοπύλαις μάχη,
got as far as Attica and took Athens, abandoned by its inhabitants save for a few who couldn't or wouldn't leave. but then he met his match at Salamis (as his fatehr Darius before him had at Marathon) where his enormous naval force was completely anihilated by the comparatively few smaller Greek boats. The story of that battle is the topic of lesson 15.

 

LEONIDAS

The Spartan leader who, betrayed (by a Greek traitor) at the Thermopylae, preferred death to the shame of falling prisoner to the Persians. His 300 fellow Spartans fell with him.
His wife is said to have handed Leonidas' shield to their son saying:
σὺν αὐτῇ ἢ ἐπὶ αὐτῇ 
The shield being  ἡ ἀσπίς, τῆς ἀσπίδος 
See Η ΠΑΝΗΓΥΡΙΣ page 98, 5th paragraph, line 5:
ἡ θεὸς λάμπεται χρυσῷ, τῇ μὲν δεξιᾷ Νίκην φέρουσα,
τῇ δὲ ἀριστερᾷ τὴν ἀσπίδα
 
Her meaning? You either win your battles and come back alive complete with your shield, or you die a hero and are brought back lying dead on your shield. In defeat soldiers threw away their weapons in order to run away faster. Coming home without your shield showed you up for what you were: a coward. And cowardice was definitely not on in Sparta.

 

THEMISTOCLES

Athenian leader who make sure the Greeks did not run away from the Persian invader but fought him by sea. An oracle had predicted that Athens could not be saved, but that ultimately the Greeks themselves would be saved by walls of wood, which Themistokles interpreted as "ships". And, thanks to Themistokles, the Greeks did achieve the seemingly impossible: they defeated the most powerful nation of the moment: the Persians, who ruled the civilized world. Britain, Gaul, Germany did not count, nor did Rome, still involved in struggles with her neighbours, trying to make it to the top in Italy.
Despite being the engineer of Athen's victory over Xerxes, Themistokles was later ostracised, like so many other famous and influential citizens - the Athenians were afraid they might become too powerful and abuse that power and therefore preferred to send them into exile till their fame had paled a little. Themistokles ended up at the court of Artaxerxes (son of Xerxes and heir to his throne) in Sousa (then capital of the Persian Empire) and finished his life among the very people he had fought so hard to keep out of Greece.