Shadow Beast
The Twilight Beast is one of the hardest enemies in Twilight Princess. They come in groups of three or five and one can never be left alive alone or else it will scream and revive the others. This fact requires that Link use the spin attack or, in his wolf form, use Midna's charge attack to take out two at once.
When attacking, Twilight Beasts will fall out of the sky from red warp portal. They then form a force field around the battleground. Any Twilight Beasts around Link will then attack him. After Link defeats them, the force field will disappear, the Shadow Beasts will break into pieces which form a new green warp portal that allows Link to use it, and many Recovery Hearts will be released.
Twilight Beasts are important to Twilight Princess because after they are defeated, they create useful warp points for Link to use.
Trivia
There seems to be two different kinds of face masks for Twilight Beasts. One, shown to the right, seems to be for lower ranking Beasts, and the other one, a rounder shinier one, seems to be for higher ranking beasts. But this is only an opinion of the author, and is in no way proven.
Gallery
Wolf Link fighting a Shadow Beast in Twilight Princess
A Shadow Beast as it appears in Twilight Princess