First off, Shurikane is character from Pocket Otaku, a webcomic/message board/overall good stuff website which all of us FJs are now members of. Cal was incessantly plugging them before our break, and for good reason. 'Shuri' is the first of a number of cameos that a lot of the PO bunch will be making in the future.
Tireless Tribe is a one-white mana, 1/1 creature. You can discard a card at any time to give it +0/+4, meaning that with a lot of cards in your hand, the Tribe can hold off nearly any offensive threat thrown at it. It's a defense machine.
Compulsion is a blue enchantment for one blue and one colorless mana. If you pay one blue and one colorless, and discard a card, you can draw a card. You can also pay one blue, one colorless, and sacrifice Compulsion (to sacrifice is to put it in your graveyard) to draw a card. This is an important card because it allows you to trade the chaff in your hand for good stuff. It's also important because Odyssey block relies so much on the graveyard, and what's in it, so Compulsion allows you to essentially get whatever you want into the graveyard at a cheap price.
Mesmeric Fiend is a great little black creature. For one colorless and one black, he's a 1/1. But when he comes into play, you can look at your opponent's hand, and remove any card (that isn't a land) in it from the game. When the Fiend leaves play, the card comes back, but he's so great because he serves as a stall tactic, and denies your opponent key cards that they may need. Even though the cards CAN come back, usually the delay that the Fiend causes is enough to cause a significant shift in the game. In this case, the Fiend 'steals' a Cephalid Looter, which is a 2/1 blue creature for two colorless and one blue which you can tap to make any player draw a card, then discard a card. Like Compulsion, this would allow Shuri to trade all of her chaff cards for good cards, while at the same time stocking her graveyard. Throw in the fact that the Looter attacks for two, and you have a very efficient little creature, that is more than worth the Fiend's time to remove.
Shuri then attacks with the Tribe, and plays a Patrol Hound, which is a 2/2 white creature for one white and one colorless mana. The Hound can also gain First Strike if you discard a card to it. I'm not going to get into a discussion as to what First Strike is at this point, because it is irrelevant to this explanation. All you need to know is that you can discard cards to the Hound. Again, we see the whole discarding and graveyard theme from Odyssey come out again. Shuri then uses the Hound's ability to discard a Wonder from her hand and get it into the graveyard. Wonder is a 2/2 Flying blue creature for one blue and three colorless. Wonder also says that if it is in your graveyard, and you have an Island in play (which Shuri does), all your creatures gain flying; that is, they can only be blocked by other creatures with flying. In essence, Wonder is more powerful in the graveyard than it is in play.
During Mingy's turn, he plays a Sonic Seizure on Shuri's Tribe. Sonic Seizure is a red Instant for one red mana that deals three damage to any target. As an additional cost to the mana, Sonic Seizure's caster must discard a card at random from their hand. What this means is that they must use some random means of discarding something from their hand. The best way to do this is to shuffle the hand, and let the opponent randomly pick one of the cards for you to discard. The Seizure kills the Hound because it deals three damage to it, and the Hound's toughness is only two, meaning it dies when it sustains two or more damage. Mingy ends up discarding an Anger to the Seizure. Anger is essentially Wonder's red cousin. Anger is a 2/2 Hasted red creature for one red and three colorless. But when it is in the graveyard and you control a Mountain, all your creatures gain Haste. Haste is the ability for creatures to attack or tap the turn they come into play, which is usually not allowed. Mingy then plays a Zombie Cannibal, which is a 1/1 black creature for one black mana. Whenever the Cannibal deals combat damage (that is, damage as a result of attacking) to a player, you can remove a card from that player's graveyard from the game. Since Mingy has the Anger in his graveyard, he can attack with the Cannibal once he plays it, which he does. It goes by unblocked because Mingy killed Shuri's Patrol Hound, and her Tireless Tribe is tapped because it attacked. Because it deals its combat damage to Shuri, Mingy can take a card from Shuri's graveyard and remove it from the game. Mingy chooses to remove Wonder, which means that Wonder's abilities go away, and Shuri's creatures no longer have Flying as a result.
Wow, that was a long explanation. I hope you all could follow it. If you have any questions, as always, feel free to drop me a line!