I will attempt to give a bit of an explanation:
There are different pesukim discussing from where our Neshama is sourced. The first is from בראשית ב, ו, concerning אדם הראשון, it says ויפח באפיו נשמת חיים. Meaning oppose to all of the other parts of creation, which comes from the speach of Hashem (עשרה מאמרות), our Neshama is coming from Hashem's breath (Metaphorically speaking of course), and the possuk uses the term breathing, to give us an understanding, (Since we can learn from people of how it exists above, being that Hashem created us in his image, as it says נעשה אדם כצלמינו כדמותינו) that just like our breath takes much more power, than when we just speak regularly, this is because our breath comes from a deep part within us. so too our souls, which is coming from the breath of Hashem is coming from a very deep part.
But how deep? That takes us to the next pessukim, where it mentions twice that we are sons of Hashem, once in שמות ד, כב saying בני בכורי ישראל. And a second time in ראה יד, א saying בנים אתם לה' אחריכם. Let's use us as the example again, being that a son comes originally from the thoughts of the father, that's the very first step. and the son is able to achieve and go way beyond a father's capabilities, shows us, that he's not just coming from the level of thought Which is revealed and is expressed by the father, but rather from a deeper part of the thought, the essence of thought, and then the son is able to express certain abilities, which the father couldn't. In this same way, being that we are Hashem's sons, We are coming from this same level of thought, from within Hashem - from the essence of Hashem's thought.
But still, this is just Hashem's thought... But since the rambam writes in יסודי התורה ב י, and in other places, that שהוא המדע והוא היודע. Meaning that by man there is 1) the person trying to understand, and 2) the subject he's trying to understand, it's two separate things. In contrast by Hashem it's all one, The knowledge and the knower, are all the same.
Therefore being that it's all one, if our Neshama is coming from the essence of the thought of Hashem. in reality, our Neshama is coming from the essence of Hashem. Hence, our Neshama is from the essence of Hashem or עצמות אין סוף.
This is only touching on the subject.