A daiyōkai (大妖怪, "Great demon") is a very powerful type of yōkai that is much stronger and smarter than common yōkai. Daiyōkai possess many different shapes and powers, with some being gigantic and inhuman in appearance, like Ryūkotsusei. Some have, or are able to assume, more human-like forms (e.g. Tōga and Sesshōmaru). It seemed that some daiyōkai became feudal rulers over vast territories, commanded armies of lesser yōkai, and constantly waged war against each other and humans alike. Most daiyōkai were supernaturally long-lived, possibly having even longer lifespans than the average yōkai.
During the series, most daiyōkai (except Tōga, Hōsenki I, Hōsenki II, and Tsukuyomaru) showed a haughty, arrogant, ruthless attitude towards other yōkai and humans, despising them for being weak in their opinion. They also saw themselves as invincible or even god-like, and were quite confident in their own skills and weapons, staying calm in even the most dire situations. Sesshōmaru was the only daiyōkai who seemed to have positively changed their point of view about humans in any sense as the series progressed.
A daiyōkai who has fully mastered their mind, body and spirit like Kirinmaru are capable of severing a body part and regrowing it. With even the severed part turning into an incarnation to serve them, if the daiyokai so wishes.
This implies that when Naraku had all but six shards of the Shikon Jewel, he was already on this level of daiyōkai sorcery. Since Naraku already had full mastery of all three; being the dominate will of multiple demons latched onto Onigumo's soul.
Sesshomaru is implied to have only mastered body and mind throughout most of the series; with his spirit mastery linked to his attachment of Tessaiga and hatred of InuYasha. Once he accepted Inuyasha the true successor to the blade, Sesshomaru wasn't only able to regrow his long lost arm, but manifested a blade of his own in it.
Sesshōmaru and Menōmaru both looked down on the Shikon Jewel, claiming their powers are greater. A Rainbow Pearl is 1/7 of Zero's demonic power, and that it took two to transform Mistress Three-Eyes similar to when Mistress Centipede ate the Shikon Jewel; given this math, a daiyōkai is averagely more than three times as strong as any powers the Shikon Jewel can grant.
Hanyō born from a daiyōkai prove more powerful than ones born to average total. Inuyasha has shown power greater than an average demon like Mistress Centipede or Shibugarasu even after they ate the Shikon Jewel.
The daiyōkai whom lead large hordes of demonic beasts go by the title of "Beast King" (獣王, "Jūō").