First off, Bryan's opponent is Sperrit in the third installment of our FJ-meets-PO saga. The little bird with Sperrit is Gira, his familiar/friend.
Thought Nibbler is indeed a fast little creature. He's a 1/1 blue flyer for one blue mana. His only catch is that when he's in play, he reduces his controller's maximum hand size by two. In other words, you would have to discard down to five cards during your discard phase.
Diligent Farmhand is a 1/1 green creature for one green mana. You can pay one green mana, one colorless mana, and sacrifice the Farmhand to search you library for any basic land card (a plains, forest, island, swamp, or mountain), and put that card into play tapped. This is what we call Mana Acceleration; anything that increases the amount of mana that you SHOULD have during that turn. The amount that you should have is based on playing one land per turn. The Farmhand also has a nice little ability in that when he is in your graveyard, he increases the power of the card Muscle Burst. But since that is not an issue in this comic, we won't be discussing it.
I explained for a previous comic what Compulsion does, and why its good, so I won't mention it here.
Minotuar Explorer is a 3/3 red creature for one red and one colorless mana. This is an incredibly good deal, and because of that, comes with a price. When the Explorer comes into play, you have to randomly discard a card from your hand, otherwise he is sacrificed (put into the graveyard). In this case, Sperrit is lucky because the randomly discarded card turn out to be a Basking Rootwalla, which he can now play for its Madness cost of 0, while at the same time fulfilling the Explorer's requirement.
If you've been keeping up with these explanations, you should already know what Anger and Wild Mongrel do, because I explained them for a previous comic.
Sperrit can attack for so much because he plays a Rites of Initiation. Rites is a red Instant for one red mana. In addition to paying the Rites' casting cost, you may discard any number of cards randomly from your hand. For each one discarded, each attacking creatures gets +1/+0. These numbers add up VERY quickly, making the Rites a very nasty card, and often a game ender if used properly. Sperrit attacks with 4 creatures: a Diligent Farmhand, a Minotaur Explorer, a Basking Rootwalla, and a Wild Mongrel. He can manage this attack because he discarded an Anger to the Mongrel, giving all his creatures Haste, and giving the Mongrel +1/+1, making it a 3/3. So there is 3 damage from the Mongrel, 3 from the Minotaur, 1 from the Rootwalla, and 1 from the Farmhand, making a total of 8 damage (3+3+1+1=8). Because he played the Rites, and discarded 2 cards, each attacker gains +2/+0, meaning that the Rites adds 8 damage to the attack, making it worth 16 (8+8=16).
Bryan, however, has a different agenda. He activates his Compulsion, and discards a Circular Logic to it. Circular Logic is a blue Instant for one blue and two colorless mana. It counters a spell unless the spells caster pays one colorless mana for each card in Circular Logic's caster's graveyard. Circular Logic, however, has a Madness of one blue mana. So Bryan discards it, but also plays it (targeting Sperrit's Rites) via its Madness, meaning that for Sperrit's Rites to resolve (for its effect to happen) Sperrit must pay one colorless mana, since Bryan has one card - Circular Logic - in his graveyard. Since Sperrit is tapped out (has no available resources) he cannot pay this cost, and Rites of Initiation is countered (its effect doesn't happen). Then Bryan blocks Sperrit's Rootwalla with his Thought Nibbler, and since Sperrit cannot pump the Rootwalla (since he's tapped out), it dies to the Nibbler, and the Nibbler dies to it, thus they "trade." So Bryan has managed to thwart Sperrit's plan, and only take 7 of the 16 damage that was coming towards him, through clever playing.