G-d is everywhere, and nowhere at the same time, everything that exists comes only from him, yet he is removed from everything at the same time.
Look at Rambam's Mishneh Torah, hilchos Yesodei HaTorah, at the beginning:
א. יסוד היסודות ועמוד החכמות לידע שיש שם מצוי ראשון והוא ממציא כל נמצא
וכל הנמצאים משמים וארץ ומה שביניהם לא נמצאו אלא מאמתת המצאו:
1: The foundation of all foundations and the pillar of wisdom is to
know that there is a Primary Being who brought into being all
existence. All the beings of the heavens, the earth, and what is
between them came into existence only from the truth of His being.
ב. ואם יעלה על הדעת שהוא אינו מצוי אין דבר אחר יכול להמצאות:
2: If one would imagine that He does not exist, no other being could
possibly exist.
ג. ואם יעלה על הדעת שאין כל הנמצאים מלבדו מצויים הוא לבדו יהיה מצוי ולא
יבטל הוא לבטולם שכל הנמצאים צריכין לו והוא ברוך הוא אינו צריך להם ולא
לאחד מהם לפיכך אין אמתתו כאמתת אחד מהם:
3: If one would imagine that none of the entities aside from Him exist,
He alone would continue to exist, and the nullification of their
[existence] would not nullify His existence, because all the [other]
entities require Him and He, blessed be He, does not require them nor
any one of them. Therefore, the truth of His [being] does not resemble
the truth of any of their [beings].
He's not some invisible thing that you just can't see because he's invisible, he transcends all time and space, and at the same time permeates all of time and space. He has no form, spiritual or physical, at all
ז. אלוה זה אחד הוא ואינו שנים ולא יתר על שנים אלא אחד שאין כיחודו אחד מן
האחדים הנמצאים בעולם לא אחד כמין שהוא כולל אחדים הרבה ולא אחד כגוף
שהוא נחלק למחלקות ולקצוות אלא יחוד שאין יחוד אחר כמותו בעולם אילו היו
אלוהות הרבה היו גופין וגויות מפני שאין הנמנים השוין במציאותן נפרדין זה
מזה אלא במאורעין שיארעו בגופות והגויות ואילו היה היוצר גוף וגוייה היה
לו קץ ותכלית שאי אפשר להיות גוף שאין לו קץ וכל שיש לגופו קץ ותכלית יש
לכחו קץ וסוף ואלהינו ברוך שמו הואיל וכחו אין לו קץ ואינו פוסק שהרי
הגלגל סובב תמיד אין כחו כח גוף והואיל ואינו גוף לא יארעו לו מאורעות
הגופות כדי שיהא נחלק ונפרד מאחר לפיכך אי אפשר שיהיה אלא אחד וידיעת דבר
זה מצות עשה שנאמר ה' אלהינו ה' אחד:
7: This God is one. He is not two or more, but one, unified in a manner
which [surpasses] any unity that is found in the world; i.e., He is
not one in the manner of a general category which includes many
individual entities, nor one in the way that the body is divided into
different portions and dimensions. Rather, He is unified, and there
exists no unity similar to His in the world.
If there were many gods, they would have body and form, because like
entities are separated from each other only through the circumstances
associated with body and form.
Were the Creator to have body and form, He would have limitation and
definition, because it is impossible for a body not to be limited. And
any entity which itself is limited and defined [possesses] only
limited and defined power. Since our God, blessed be His name,
possesses unlimited power, as evidenced by the continuous revolution
of the sphere, we see that His power is not the power of a body. Since
He is not a body, the circumstances associated with bodies that
produce division and separation are not relevant to Him. Therefore, it
is impossible for Him to be anything other than one.
The knowledge of this concept fulfills a positive commandment, as
[implied by Deuteronomy 6:4]: "[Hear, Israel,] God is our Lord, God is
one."
In truth, everything is Hashem, nothing exists on its own, everywhere you look, you are seeing only Hashem.
The difference between Hashem and everything else, though, is that Hashem made the world in a way that you don't realize that you're only seeing Hashem, He made it in a way where you think you are seeing a separate world, and because of that Hashem might be imagined as just some "invisible figure" who is somewhere far away watching us, but that in fact is not true at all, since everything that exists is actually only Hashem, it's only that we don't see it OR realize it. (Tanya part 2 chapter 3).
The part of Hashem that was put into man, though, is really just a direct link to Hashem. Meaning, in reality, everything is in fact equal to the divine spark within us, there's no difference between it and everything else, since everything is Hashem and Hashem in everywhere and in every thing completely equally, but the power we have with the divine spark is that even though we are in a world which seems SEPARATE, but the divine spark within us has the power to be brought out, and we will NOTICE Hashem in that divine spark, and even more, that divine spark gives us the power to reveal the truth of Hashem in the rest of the world as well (see the end of the last linked source, from 5741).
In other words, the divine spark is something that has the power to be felt directly by us that it is Hashem's essence. In reality, everything in the world is Hashem, but He's hidden within it, and it's hard to realize, but all the divine spark is is Hashem's DIRECT revelation in us, in a way that we can realize.
See, for starters, this part of section 2 in the Maamar "בס"ד. אור לה' סיון, ערב חג השבועות, ה'תשמ"ט"
דבריאת שמים וארץ מתחדשת בכל רגע ורגע, כתורת הבעש"ט עה"פ11 לעולם הוי'
דברך נצב בשמים (הובא בספר תניא קדישא12) שכח האלקי מהוה תמיד את הנברא
מאין ליש. ומכיון שבריאה והתהוות יש מאין היא בכח העצמות, מובן, שהבריאה
שבכל רגע ורגע היא יש מאין ממש מהעצמות.
It says that everything is (constantly) being renewed from Hashem's direct essence, so in reality, everything is Hashem.
In more of a DIRECT answer to your question concerning Tanya's description of Hashem "blowing the soul into man" and what that means, see section 5 of the Maamar בס"ד. יום ב' דראש השנה ה'תשמ"א here:
ה) ויש לומר שזהו מ"ש אדמו"ר הזקן בענין ויפח באפיו נשמת חיים, שהוא
בבחי' נפיחה בכח כביכול, דזה שצריך להיות נפיחה בכח הוא מפני ששרש
הנשמה הוא בבחי' העלם העצמי, העלם שאינו במציאות, וההמשכה מבחי' העלם
שאינו במציאות היא ע"י טרחא ויגיעה דוקא. דהנה ידוע שבכדי להמשיך מהעלם
שישנו במציאות אין צריך לטרחא ויגיעה. וכמו שלהבת הקשורה בגחלת, דלהיות
שגם בתוך הגחלת היא במציאות אש אלא שאינה נראה ונגלה בחוץ (העלם שישנו
במציאות), לכן הוצאת השלהבת מהגחלת היא בלי עמל ויגיעה. משא"כ ההמשכה
מבחי' העלם שאינו במציאות היא ע"י טרחא ויגיעה דוקא. וכמו הוצאת האש מצור
החלמיש, דלהיות האש שבצור הוא בבחי' העלם שאינו במציאות, לכן אי אפשר
להוציא ממנו אש כ"א ע"י הכאה, בטרחא ויגיעה דוקא. וכמבואר כ"ז בארוכה
בדרושי כ"ק אדמו"ר (מהורש"ב) נ"ע. וזהו מ"ש אדה"ז שויפח באפיו נשמת
חיים הוא בבחי' נפיחה בכח, כי שרש הנשמות הוא בבחי' העלם שאינו במציאות,
בחי' צור [וכמבואר בלקו"ת בענין התשובה דוהרוח תשוב אל האלקים אשר
נתנה, דבחי' האלקים (אשר נתנה) שהוא שרש הנשמה (ומבחינה זו ניתנה הנשמה
באופן דנתינה, דכל הנותן בעין יפה הוא נותן) הוא בחי' צור], ולכן
ההמשכה משם היא
ע"י נפיחה בכח. ולהיות דשרש נש"י הוא בעצמותו ית' לכן ביכלתם להמשיך
בעולם גילוי עצמות אוא"ס.
If your Maamer Hebrew still needs some improvement, I can attempt to translate / explain the basic idea of what it's saying, but you should somehow read it word for word inside yourself, like maybe have someone help you read it.
Anyway it's basically saying that when the Alter Rebbe said that "He blew into him the soul of life" the fact that he said "he blew", implies a powerful breath (not just like words of speech, although he doesn't say that here in the Maamer), and since it was blown from Hashem in a powerful way, that means it comes from Hashem's innermost essence. Then he goes on a little to explain what is this innermost essence, and compares it to the power of fire that exists in a flint stone.
Unlike a coal, where the fire is actually IN the coal directly (since, after all, it's hot and sizzling), and in order to get the fire out of the coal, all you have to do is breath on it lightly [which is like words of speech,(Maamer in 5666 that's quoted in note 48 of this Maamer, (ד"ה ואברהם זקן תרס"ו (המשך תרס"ו ע' פ ואילך).)], but a flint stone requires you to hit it to bring out the fire, because the actual fire doesn't really exist within the rock fully, only in potential; in other words, it's more deeply rooted within the essence of the rock, and the power of fire within it isn't revealed openly, before you hit it (unlike the coal which is already hot and sizzling before you blow on it, which shows that the connection of the fire with the essence of the coal isn't so strong, since it can be brought out easily), so since the fire in the flint stone is completely united with it's essence, it needs to be hit hard in order to bring it to the surface, so he explains in this Maamer (and the one from 5666 that was mentioned earlier) that so too was Hashem's "breathing" of the soul into man "with power" (as mentioned in Tanya), since the soul is united deep within the essence of Hashem "Tzur Chayeinu -- our "Rock" of life", just like the fire in the flint-stone, so Hashem needed to blow it out with power in order to bring it into the body of Man, similarly to how one needs to hit the flint stone very hard to bring out the fire within, since it's so deeply rooted in it.
Then, after he explains how the source of the Soul is in the Essence of Hashem, he says that it therefore has to power to reveal the Essence within the world as well.
That's the basic idea but you should look up that entire linked Maamer and look up all of the notes with a Rabbi, especially that paragraph, to fully grasp the idea.
