Rabbi Akiva said: This is a cardinal principle of the Torah. (Midrash Rabbah)

You shall not steal; neither shall you deal falsely, nor lie to one another. You shall not swear by my name falsely, and profane the name of your Elohey. I am YHVH. ‘You shall not oppress your neighbor, nor rob him. The wages of a hired servant shall not remain with you all night until the morning. You shall not curse the deaf, nor put a stumbling block before the blind; but you shall fear your Elohey. I am YHVH. You shall do no injustice in judgment: you shall not be partial to the poor, nor show favoritism to the great; but in righteousness shall you judge your neighbor. You shall not go up and down as a slanderer among your people; neither shall you stand against the life of your neighbor. I am YHVH. You shall not hate your brother in your heart. You shall surely rebuke your neighbor, and not bear sin because of him. You shall not take vengeance, nor bear any grudge against the children of your people; but you shall love your neighbor as yourself. I am YHVH." (Vayikra/Leviticus 19:11-18)

To love a fellow is to love Elohim. For "You are children unto YHVH your Elohey" (Deuteronomy 14:1); one who loves a father loves his children. "Love your fellow as yourself" is an elaboration and elucidation upon "And you shall love YHVH your Elohey " (Deuteronomy 6:5). When one loves one’s fellow one loves Elohim, for one’s fellow contains within himself a "part of Elohim above" (Job 31:2). By loving one’s fellow, the innermost part of him, one loves Elohim. (Rabbi Israel Baal Shem Tov)

A gentile came before Shammai and said to him, "I wish to convert to Judaism, on the condition that you teach me the whole Torah while I stand on one foot." Shammai drove him away with the builder’s cubit which was in his hand. When he came before Hillel, Hillel said to him: "What is hateful to you, do not to your neighbor. This is the entire Torah; the rest is the commentary—go and learn it." (Talmud, Shabbat 31a)

Why did Hillel say that this is "the entire Torah"? Granted that it is the essence of all mitzvot governing our behavior "between man and man"; but the Torah also includes many mitzvot that are in the realm of "between man and G-d." In what way is the mitzvah to "Love your fellow as yourself" the essence of mitzvot such as praying, or ceasing work on Shabbat?
The explanation can be found in the answer to another question: How is it possible to love another "as yourself"? Are not self and fellow two distinct entities, so that however closely they may be bound, the other will always be other, and never wholly as the self?
As physical beings, one’s self and one’s fellow are indeed two distinct entities. As spiritual beings, however, they are ultimately one, for all souls are of a single essence, united in their source in G-d. As long as one regards the physical self as the true "I" and the soul as something this I "has", one will never truly love the other "as oneself." But if the soul is the "I" and the body but its tool and extension, one can come to recognize that "self" and "fellow" are but two expressions of a singular essence, so that all that one desires for oneself, one equally desires for one’s fellow.
Otherwise stated, the endeavor to love one’s fellow as oneself is the endeavor to cultivate one’s own spiritual identity; to see the soul and spirit as the true and ultimate reality, and the body and the material as extraneous and subservient to it. This is the entire Torah. (Rabbi Schneur Zalman of Liadi)