Agamemnon was the most powerful king in Greece and the commander of the Greek forces in the Trojan War. The king of kings pops up in lots of myths, and most of the time he's a total jerk. (Check out the Iliad for lots of examples of Agamemnon's bad behavior during the Trojan War.) Overall, Agamemnon represents the power-hungry tyrant, who'll do anything to keep his power.
In this story, we see Agamemnon before the war kicks off. Guess what? He's a jerk then too. He sacrifices his daughter Iphigenia to appease Artemis, who's mad because he killed a deer in her sacred grove and bragged about it. The goddess refuses to let the wind fill the sails of the Greek fleet until she has Iphigenia, and the king totally obliges. If the fleet doesn't sail, Agamemnon will look like a total loser, so it's the chopping block for Iphigenia, even though the whole thing is her dear old dad's fault. How is that fair, you ask? Answer: it's not.
Eventually, however, Agamemnon gets what's coming to him. All that power he fought so hard to keep doesn't mean doodly-squat when he gets home to Mycenae. Instead of dying in battle, like a good warrior king should, Agamemnon gets stabbed to death in a bathtub at by his wife, Clytemnestra, who's been stewing on Iphigenia's murder for years. Although Clytemnestra is often shown as a villainess herself, she can also be seen an instrument of the gods' justice. She is the thing that finally punishes Agamemnon for his pride and lust for power.
Clytemnestra comes off a lot differently depending on who's talking about her. If you asked ancient writers in the anti-Clytemnestra camp, she's an adulterous queen who sleeps with her husband's cousin while he's off at war and murders the dude when he gets home. Her son, Orestes, who later kills her for Agamemnon's murder, would definitely agree with this point of view. There's no getting around the fact she's totally guilty of regicide (killing a king) and mariticide (killing a spouse). If she committed these crimes today, she would probably be locked up for life and might even face the death penalty, depending on where she lived.
Just to play devil's advocate, though, Clytemnestra does have a lot of reason to be majorly ticked off at Agamemnon. For one, the only reason Clytemnestra is married to the guy is because he killed her former husband and claimed her as a prize. (Romantic.) On top of that, he honors that marriage by sacrificing their daughter Iphigenia to make up for his own crime against Artemis. Not that we're condoning murder of anybody for any reason, but you can kind of see where Clytemnestra was coming from. Her husband was about as bad as a husband can be. While it's easy to pigeonhole Clytemnestra as an evil murderous adulterous, you can also see her as a woman finally asserting power over a man who treated her like total crap.
Agamemnon and Clytemnestra's oldest daughter definitely gets the raw end of this deal. Her father sacrifices her to Artemis to atone for his own crime against the goddess. The virginal girl is totally innocent of doing anything bad like ever, so it's a bummer that she's got to die. Ironically, it's Iphigenia's very innocence that makes her a fitting sacrifice for Artemis. Though the goddess was sometimes thought of as a protector of young virgins, many of her cults were know to offer virginal girls as human sacrifices to their goddess.
Interestingly, in some versions of the story, Iphigenia is saved by Artemis at the last second and replaced on the altar by a young deer. Iphigenia is then whisked away to a place called Tauris, where she becomes a priestess of Artemis, and performs... guess what? Human sacrifices. Man, that Artemis just doesn't quit.