The Arrancar were the antagonists that enthralled a number of readers with Bleach. They were Hollows who had removed their Masks to regain their Human forms, and who had sealed the power of their souls within Zanpakuto. When an Arrancar released their Zanpakuto in what is called "Resurreccion", the power of their soul - their original Hollow form - is restored to them. In doing so, the Arrancar gain access to their abilities, their combat power is multiplied, and their reiatsu level increases.
As Urahara described it in the recent arc, the Resurreccion is akin to a Bankai in its function. The Bankai is the second release of the Zanpakuto, requiring one to subjugate their Zanpakuto spirit in order to learn its name. Given that the Stern Ritter were able to steal the Bankai with the Star Medallion - an act indicated to steal the Zanpakuto Spirit as well - it means that the Bankai is the full manifestation of the "power of the soul" of the Shinigami.
However, the Arrancar Saga showcased two forms that appear to be above these two releases: the Segunda Etapa and Ichigo's Mugetsu.
The Segunda Etapa seemingly came out of the blue in Ulquiorra's fight with Ichigo. As if beating him down with Murcielago was not enough, Ulquiorra went a step beyond the Resurreccion of any Arrancar seen before him or since then and revealed the Segunda Etapa - a "Second Stage" to the Resurreccion. As Uryu described the reiatsu of the Segunda Etapa, it was not simply the power of the reiatsu released by Segunda Etapa that was different - there existed a fundamental difference in its reiatsu. To be specific, Uryu described the reiatsu as feeling like "there's an ocean coming down on him", and that it was too thick and dark to be considered "reiatsu".
Ichigo's Mugetsu is the name given to the form he took when activating "The Final Getsuga Tenshou", a technique that caused Ichigo to lose all his Shinigami power upon activation. What must be noted is the change in form. Not only did Ichigo's Shihakusho undergo a radical change into a blue-gray binding around his body and mouth, but his physical appearance changed as well - his hair turned long and pitch-black, and there were markings on his arms as well. Although Aizen could not sense him in that state, I can imagine that there was a fundamental change in the nature of his reiatsu as a result of activating the technique.
I believe Ichigo's Mugetsu provides the key to understanding what happened with the Segunda Etapa, and where that power came from. When Ichigo exited the Dangai after completing his training to attain the "Final Getsuga Tenshou", we observed that Tensa Zangetsu had agglutinated itself to Ichigo's right arm. While a similar evolution to Aizen's Transcendence, the purpose was fundamentally different. When Ichigo activated the Final Getusga Tenshou, Tensa Zangetsu vanished and was replaced by a stream of spiritual power emanating from Ichigo's right arm. As Ichigo described it, "he became Getsuga", meaning Ichigo had "become one" with his Zanpakuto and its power.
I believe this is connected to Segunda Etapa because a very similar transformation occurred when Ulquiorra activated it. His Hollow hole widened and a blood-like marking poured down from the hole, the markings on his face change and the whites of his eyes darkened to a green colouration, his wings transformed, the robe of his Resurreccion vanished, he grew a tail, his feet became bat-like, and his arms and lower body became covered in a black fur.
To those of you paying attention to the description, you'll notice I left something out. I did so because it is crucial to my point.
When Ulquiorra released the Segunda Etapa, his Mask Fragment completely vanished, and in its place are a set of horns on his head.
As implied in Neliel's flashback, the Mask Fragment is very important to the Arrancar. Neliel was aghast when she saw Pesche and Dondochakka's Mask Fragments ripped completely off, and she lost all her power and turned into a kid when Nnoitra severely damaged her Mask. Szayel speculated that the phenomenon happened due to her reiatsu flowing from her broken Mask. Based on the scene in Kirinji's Hot Springs, the core of one's reiatsu is located in their head of Shinigami. The same is likely true for Arrancar, since the blow that cause Neliel to revert to a child was to the head.
As we learnt in "The Lost Agent Arc", the Hollow's "lost heart" becomes their Mask, their physical appearance, and their power. In a sense, the Mask is the core of a Hollow's power. By extension, while an Arrancar's Zanpakuto is the "power of the soul" sealed into the blade, the Mask Fragment of the Arrancar is still part of "the core of their power".
I believe that the Segunda Etapa is more than just a 'second release' - it is the Arrancar "becoming one" with their power. I believe that an Arrancar must be able to release the power that is still contained within the Mask Fragment in order to achieve Segunda Etapa. In doing so, their Human bodies themselves take on a more animalistic appearance akin to but different from their original Hollow form. Just by comparing Ulquiorra's Segunda Etapa to his original Hollow form from UNMASKED, you can see that it is the original Resurreccion which bears more of a resemblance to his original Hollow form, leaving the Segunda Etapa a form beyond their original Hollow selves - one which is a result of the complete unification of their Hollow and Human selves.
While Arrancar may have Shinigami-like powers such as Sonido, Pesquisa and the Arrancar Zanpakuto, the Arrancar are not Shinigami-Hollow hybrids - the powers they gain are only "similar" to the Shinigami - but are "Human-Hollow". It should be clear where this idea comes from - "Hollows" breaking their Masks to regain their "Human" forms and sense of reason. In this sense, the true opposite to an Arrancar is a Fullbringer - "Humans" who are born with power derived from "Hollow" reiryoku.
As Urahara explained in "Everything But the Rain", "Humans" are opposite of "Hollows". By breaking their Masks, "Hollows" break down the boundary between themselves and their opposite. Thus, the Segunda Etapa is the result of the Arrancar's "Human" self 'becoming one' with their "Hollow" self - "the core of their power". The reason why Ulquiorra's reiatsu felt so different is because a fundamental change in his nature occurred at that point - there was no distinction between "Human" and "Hollow" anymore.
At the end of the day, "becoming one" with your power appears to be the true final stage of development in one's abilities, but it is so powerful and rare that only very few people can perform it - much less have knowledge of it.