Why do we call G‑d "Father" on Rosh Hashanah? Why not "Mother"?
To the Jewish mind, G‑d is both here and beyond here at once. Philosophers call that immanence and transcendence. Many of them say that He can't do both at once, but we say who are you philosophers to tell G‑d what He can be and what He can't be?
When we refer to G‑d's presence within our world, giving life to all things, then She is the Shechinah. When we refer to G‑d's transcendence beyond this world, we call Him "The Holy One, blessed be He." G‑d does not change or have parts, G‑d forbid. Both are the same one and singular G‑d, just looking at that G‑d from different angles. From one angle you see a modality of being deeply involved and immanently there; from another angle you see Him in a modality of being absolutely beyond all things and transcendent even of existence itself.
In our prayers, we--all of us together as one--take the role of the Shechinah petitioning the Holy One, blessed be He. In a way, G‑d is speaking to Himself. That is why we ask at the beginning of the Amidah, "G‑d, open my lips so that my mouth may speak Your praises." We are asking G‑d to speak to Himself through us. We can't pray to Him as He is the Shechinah because it's His Shechinah that's doing the praying.
Our mitzvahs, study and prayer unite these two aspects of G‑d into a perfect whole. Studying Torah is a way for G‑d's transcendence to enter our world. Our prayers are a way that His presence in our world reaches upward towards transcendence. Each mitzvah in its particular way creates a harmony between the two aspects.
Much of the Zohar is dedicated to illustrating this concept. The prophets also allude to it in their ubiquitous use of the husband/wife metaphor. In many prayer books you will find instructions to say before a certain mitzvah, blessing or prayer, "For the sake of the union of the Holy One, blessed be He, and His Shechinah, in the name of all Israel."
This is also the meaning of the phrase, "On that day, G‑d will be One and His name will be One." Of course, He was already One before the world got started and remained One after creating it. We are talking here of how the created beings of His world tune into that oneness, by discovering a harmony between the two aspects that we have to deal with. G‑d will be One is about how He is way beyond our world extending into how He is present in our world. His name will be One is about how He presents Himself here revealing a harmony with how He is totally beyond.
I better stop before things get totally foncusicated. These are things discussed at length in many profound treatises on Kabbalistic thought. If you want some reading material, let me know and I'll plug you in.
Have a great, sweet year in 5770!