HaShem made the human being with free will (to choose), but what does it mean to HaShem, or what does He gain/benefits from making the human being and why make this human being with the ability to exercise free will and making his own choices?
(HaShem already seems to have messengers to accompany Him and serve Him, for example).
I'll quote a bit from Rabbi Kaplan's handbook of Jewish thought chapter three entitled Man. See there for his sources.
3:4 Since God is absolutely perfect in Himself, it is obvious that He had no inner need to create the universe. It must be concluded that God's creation of the universe was a most perfect act of altruism and love. It is thus written "The world is built of love" (Psalms 89:3)
3:12 Man was therefore created as a creature capable of to some degree understanding, and ultimately experiencing, the greatest possible good, which is God Himself. It can therefore be said that God's purpose in creation was to allow Himself to be experienced by a creature far removed and much lower than Himself. It is thus taught that God created the universe because "He desired an abode in the lower world". (Tanchuma Naso 16)
3:13 God caused man to have a psychological makeup with which he would experience the greatest possible pleasure in doing something that he knew to be good and beneficial. This pleasure is enhanced according to the importance of the authority declaring that a given action is good. Since God Himself is the highest possible authority, there can be no greater pleasure in performing a job well done than in knowingly obeying the expressed will of God.
3:15 Obedience to God's will therefore fulfills His altruistic purpose in creation.
3:16 In order to enjoy the pleasure of such accomplishment, it is imperative that man know that his accomplishment is a matter of his own free choice, and not the result of his nature of compulsion. So that all choices of action be up to the individual, God gave man absolute free will.
There are really two ways to look at this question. One way is "what purpose is served through the creation of man," which is what the other answers have addressed. The other way to ask the question is "what was Hashem's motivation in deciding to create man?"
This second question is what the Rambam describes as having no "real" answer. The Rambam writes in Moreh Nevochim 3:13, after pointing out the difficulties in identifying the purpose (תכלית) of creation, what the inevitable conclusion must be:
ואם תאמר אין זה לשלמותו אלא לשלמותנו, לפי שכך הוא הטוב לנו והיא שלמותינו, תתחייב השאלה עצמה ומה תכלית מציאותנו בשלמות זו? והכרחי הוא שיסתיים הדבר במתן התכלית שכך רצה ה' או כך גזרה חכמתו, וזהו הנכון
And if you will say that [creation of man] is not for the sake of His perfection but rather for our own, as this perfection is the best thing for us, this necessarily begs the question - what is the purpose of our existing with this perfection? And one must conclude by giving the reason that this is what Hashem wanted or this is what His wisdom decreed. And this is correct...
Indeed, answering, or even asking, the question would really be an infringement on the absoluteness of Hashem's existence and His kadmus (exclusive primordiality), as seeking a reason why Hashem would want to create the world implies the existence of something external from Himself which would influence His decision. R' Yosef Alcastille makes this point explicitly (in a letter quoted by the Shela"h in Beis Hashem):
ואם תשאל טעם לרצונו של מקום אתה שואל אם יש סיבה למעלה ממנו שתעורר אותו לעשות זה
And if you ask for the reason of Hashem's will, you are asking if there is a cause above Him which aroused him to do this.
I can't tell you for sure that the Rambam would include this in במופלא ממך אל תדרוש - that which is beyond you do not seek (Chagiga 13b, see Moreh Nevochim 1:32), but it certainly seems reasonable to call it such.
to answer part of the question
from the chovos halevavos gate 4 ch.3
"That one is conscious of G-d's abundant goodness to man, and how He brought him into existence out of abundant and pure benevolence and kindness, without man being worthy of this, nor because G-d has any need for him, but only out of generosity, benevolence, and goodness"
hence, God does not gain anything. It is pure altruistic benevolence
G-d is in need of nothing. G-d did not create people so that they can commune with G-d, and the idea that G-d did so because G-d loves people, is pure nonsense. G-d is all-powerful and needs nothing. In short, G-d does not benefit from us. The notion that G-d somehow needs our help is mystical, wrong, and if nothing else, insulting.
