Twili
The Twili is a race of beings who inhabit the Twilight Realm. Most of the inhabitants are of the "monster" variety throughout your adventure, due to Zant's evil rule. However their true forms are more impish in nature with black and red markings while other members of the race have more human like bodies like Zant and Midna.
Background
Eons ago, the Twili were a tribe of Hylians that was sent to the Twilight Realm by the Sages of Hyrule as punishment for their misgoverned attempt to use old magic to claim the Triforce. Their "old magic" became known as the Fused Shadows, a powerful instrument, however, their powers proved too weak for the power of the gods. They were banished and their Fused Shadow were split into three pieces and scattered throughout the two realms, The Twilight realm and Hyrule. This tribe lived in the Twilight Realm for centuries until evolving, mere shadows of what they once were, the Twili tribe became used to their surroundings and came to accept their fate. While some came to love the beautiful peace that can be found only in Twilight, it drove some of it's inhabitants mad. After centuries of rule, Midna became just one of many rulers in a long line of royalty, the Twilight Princess. It was around this time that a rebel force grew from within the Twilight, spearheaded by Zant. It is revealed that Zant was next to become Twilight Ruler, but was passed over. In a terrible rage, he used the power of his false-god, Ganondorf, to transform most of the inhabitants of Twilight into monsters. Zant also transformed Midna into an imp creature. Midna's only hope was to find the magic of her ancestors, the Fused Shadows, and use it against Zant.
Timeline, Ocarina and Majora's Mask
The events described in Twilight Princess were not specified as occurring before or after the events of Ocarina of Time, officially the first Zelda game in the timeline, it is also never made certain, although hotly debated weather or not the Twili had any inclusion the events that lead to the creation of Majora's Mask as one would assume that the Mask was also forged before the events of Ocarina of Time.
Debates arose when similarity between the design of Midna and Majora's Mask were spotted by a number of fans, and now many players choose to believe or speculate that the Twili are in fact responsible for creating Majora, in a separate attempt to obtain the Triforce.