Initially, the fun is in all the delightful matchups that occur. For example:
An elite band of mindflayers vs a horde of monkeys with sticks.
An army of Aztec were-jaguars backed up by Hobbit-crossbowmen, facing off against an equal army of Nordic werewolves and spell-casting garden-gnomes
A castle siege that is going poorly for the attackers, until their mages cast flight on a group of magically tamed lions, sending them over the walls and into the enemy's archer formations. RAWR!
As you can see, a lot of the enjoyment of the game comes from having an active imagination.
It is also neat that the player has an actual representation in the game. This is great for trash-talk and for telling stories. Again, maybe this is just my active imagination, but it is fun when you manage to blind your opponent's Cyclops pretender, or when your oppponent's Manticore is trapped in a castle, catches a disease from lack of food, and then has its stinger fall off.