Question: In Tanya [the central text of Chabad Chassidism and written by the Alter Rebbe] it speaks about different heavens, like one in which Manna is ground for Tzaddikim. Regarding the Shema, I was taught to have in mind that Hashem is One in the seven heavens and on earth. What do we learn for our service of Hashem from these ideas about heavens?
Answer: When we declare that Hashem is One in the heavens and on earth, our intent is that there is no true existence other than Hashem. For example, when an artisan crafts a container, the container continues to exist even after the artisan removes his hands. With Hashem's creation this is not so. Without Hashem's constant vivifying life force - creating everything constantly from "nothing to something" - creation would cease to exist. Just as there are many heavenly dimensions (as mentioned in your question), so too "...in each world there are creatures without limit or end, myriads upon myriads of various grades of angels and souls, and so on." (Tanya, chp. 51). The vastness of creation is not a contradiction to Hashem's unity, but enhances our awe of the Creator.
This Divine life force is referred to as speech. As we say in davening, "Blessed is He who spoke and the world came into being..." While the source of each Jew's soul is rooted in Divine "thought" — the innermost level of G-dliness — all other created beings, even angels, are created by Divine "speech". Speech is external in comparison with thought. (Tanya, chp. 2)
In Kuntres HaTefila (authored by the Rebbe Rashab) we learn that to arouse true love and awe of our Creator, we must contemplate G-dly concepts in detail. For example, briefly contemplating the general idea that Hashem enlivens creation every moment will most likely only create a temporary emotional arousal. However, when one contemplates in detail the vastness of the physical and spiritual realms; that Hashem is sustaining all of creation every moment; and that Hashem's essence is infinitely more exalted than this life force, he will be more capable of experiencing a deeper and lasting love and awe.
Love and fear (awe) motivate our G-dly service. In fact, Tanya compares love and fear to wings - elevating our Torah and mitzvot to higher spiritual realms. Thus, the more we comprehend and appreciate the vastness of creation (including the many heavens, as mentioned in your question) and the loftiness of our Creator, the more passionate will be our service of Hashem.