The true nature of the divine self is difficult to conceptualize or explain. I do not wish to embroil myself or the reader in an abstract and convoluted philosophical discussion. Instead, I will focus on two illustrative text samples, drawn from the vast corpus of Chabad Chasidic thought.
The first statement is from Hemshech Samach Vov (Vayolech Hashem Et Ha-yom, P.223), by Rabbi Shalom DovBer of Lubavitch.
"The concept of infinitude (ain sof), literally without limitation, is that no property can be ascribed to the deity, and the deity cannot be defined with any description at all... Even the most wonderful and lofty description cannot be applied - even the description "without limit." Conversely, one cannot preclude anything from the deity, for the deity carries all things (potentially but not actually...) and the deity is precluded from everything. This is the concept of infinitude (ain sof): the preclusion of any description; the preclusion of limitation; the preclusion of any affirmation and the preclusion of any negation; the inclusion of all by default. All this is only possible for the very essentially of the divine self (bechinat ho-atzmut mamash), whose being is of its own self, and who is the true being whose being transcends actual being (aino be'bechinat metzi'ut nimazah)."The second selection is from Kuntras Mai Chanukah (P. 24), a compilation by Rabbi Yoel Kahn from the talks of Rabbi Menachem Mendel Schneerson. The context here is the famous question of the Beit Yosef as to why eight days of Chanukah are celebrated; if there was actually enough oil for one day apparently no miracle occurred on the first day? The following answer is offered:
"Since the miracle was made in order that the lighting of the menorah could be done in the finest possible way (for according to the law they were entitled to light using impure oil, [and a miracle was unnecessary, accept to allow them to avoid any legal lope-holes]), it makes sense to say that the miracle occurred in a form that allowed the oil to remain completely natural oil [as prescribed by law], without any quantitative or qualitative addition.
In other words: When the Beit Yosef writes "that they found the lamps filled," the intention is not that the oil was first burned up, and afterwards new oil was created ("miracle oil"), but that the miracle was that the oil had never been burnt up at all, just like the burning bush about which the verse says, "behold the bush burnt in fire, and the bush was not consumed." Accordingly, they fulfilled the commandment to light the menorah with completely natural oil, which remained utterly unchanged (not quantitatively or qualitatively).
According to this explanation, the combination of the natural and the miraculous is further highlighted. It transpires that the very fact that they had natural oil specifically was achieved via a wondrous miracle that completely transcends the limitations even of a regular miracle. The light of the lamps must come from the oil, and the oil must be turned [by combustion] into fire and light. If the oil is not consumed it follows, however, that the light did not come from the oil. If so, we must say that the miracle was such that although the oil was turned into fire and light, it nevertheless remained untouched. This is a most transcendent miracle, simultaneously embodying two mutually-exclusive events. It transpires that through a completely transcendent miracle specifically they were able to light the oil with completely natural oil."For a fun, humorous, entertaining, deeply illustrative and thoughtful re-imagining of how this miracle occurred see The Menorah Files by Rabbi Tzvi Freeman.