Who exactly are the Otsutsuki clan in Naruto? Back when Naruto was rapidly hurtling towards its final arc, many fans predicted that either the ancient Madara or Naruto's ongoing rival, Sasuke, would be the final villain. Instead, Masashi Kishimoto took his entire audience by surprise, introducing a new character that swiftly put down Madara and assumed the position of arch-antagonist right as the story looked to be coming to a close.
Kaguya Otsutsuki is revealed as the catalyst for almost every major event in the Naruto series and although the final battle in the series is, as predicted, Naruto vs. Sasuke, Kaguya is the ultimate true villain of the piece. Unfortunately, Kaguya was unveiled very late in the story and has a relatively complex origin story, leaving some fans confused as to exactly what Kaguya was, what she wanted and where she came from. The anime made attempts to fix this with extended flashbacks, but the reality-bending mythology of the Otsutsuki clan has continued to expand even after Naruto's conclusion, furthering their sense of mystery.
Members of the Otsutsuki clan possess a natural ability to travel between dimensions and have been constantly moving between worlds since ancient times. Their home dimension has not yet been revealed, and it's possible that the clan have been in transit for so long that their place of origin has been either destroyed or forgotten. The Otsutsuki travel in pairs and seek out God trees - natural occurrences that appear in multiple dimensions. From these special trees, chakra fruit can be harvested, and eating these tasty treats is how the Otsutsuki maintain their power and extended life.
In terms of the Otsutsuki's presence on Earth, Kaguya arrived with her partner (whose fate is revealed in the Boruto sequel series) and began cultivating chakra fruit as usual, but she developed a strange attachment to the human way of life. The future villain broke off from the other Otsutsuki, sought to claim Earth as her own and was worshiped as a goddess by mankind. Sadly, Kaguya's desperation to maintain her power turned humanity and her own family against her, and she was eventually sealed away by her own sons. Through Kaguya's descendants, the ability to manipulate chakra was passed throughout the population and became known as ninjutsu, while the God tree was split into nine parts as a precaution. These pieces are the nine tailed beasts seen throughout the Naruto world. After Kaguya was defeated, Momoshiki and Kinshinki Otsutsuki were sent to Earth to discover her fate - events explored in Boruto: Naruto The Movie.
Chowing down on chakra fruit gives members of the Otsutsuki clan extraordinary speed and strength, as well as almost complete mastery over the chakra-based attacks that humans would refer to as ninjutsu. Otsutsuki also have an affinity for Kekkei Genkai - techniques usually limited to certain bloodlines. For example, Kaguya possesses the Hyuuga clan's Byakugan, the Uchiha clan's Rinne Sharingan and the bone-based jutsu used by Kimimaro.
Unfortunately for Naruto and his pals, the Otsutsuki have a habit of lingering on after death. While this can at times be useful, such as when the Sage of Six Paths passed his abilities onto Naruto and Sasuke, it can also be rather troublesome. Kaguya, for instance, could only be permanently sealed away, rather than defeated. And even though the combined forces of the Five Kage and Sasuke managed to put down Momoshiki, his spirit lingered on long enough to inflict Boruto with a mysterious curse mark known as Karma.
While the Otsutsuki clan only appeared at the very end of Naruto, they inform a large part of the story and are a near-constant presence in the Boruto series. Fans certainly could've used some more explanation and build-up to their first appearance, but at least the Otsutsuki legend is being continued in Boruto.