The commandment “You shall love your fellow as yourself,” requires us to be as concerned about others as we are concerned for ourselves, and even to wish more for others than we have ourselves.

The commandment to love someone “as yourself,” contains an element of hyperbole, and its meaning is that we must desire good for others:

The explanation of “You shall love your fellow as yourself,” is that it is an exaggeration, as one could not undertake to love another as much as he loves himself; and furthermore, Rabbi Akiva taught, “Your life takes precedence over the life of the other” (Bava Metzia 62a). Rather, the mitzva, from the Torah, is to love one’s fellow in every matter, just as he loves himself, [wishing] everything good for himself.

The commandment to love one’s fellow is a commandment against being envious of others:

It is possible that it [literally] says not “You shall love your fellow as yourself,” but rather “You shall love to your fellow…” in order to equate them, meaning that the two loves [one’s love for others and his love for himself] should be equal in a person’s mind. Because sometimes, one’s love for another person extends only to certain areas, e.g., he wants the best for the other person with regard to wealth but not with regard to wisdom. But if he loves his fellow in all matters, he will want the beloved to have wealth, possessions, honor, knowledge, and wisdom, and he will not just equate himself to him, but will want him to have more than he himself has, in all spheres. The verse commands us not to carry this abhorrent attribute, envy, in our hearts; rather, we must love another, wishing all good things upon him, as a person does himself, and not set limitations upon this love. (Ramban, Leviticus 19:18)

An absolute connection between two individuals is expressed through making a covenant. This means that they are not separate from one another. They assist each other in every matter, to the point where they do not feel like distinct entities. The Torah commands us to love one’s fellow in the same manner: One should feel as though he is not distinct from us; rather, he is an inseparable part of us.

Two people who make a covenant are as one body while they are alive, and only death can part them. Therefore, if a person feels that some harm or sorrow has come to someone with whom he has made a covenant, he will exert himself in order to save him, just as he would endanger himself. Likewise, he will not hide from this person any knowledge or sense that others are planning on harming him, or that others have thought badly of him. So too, he will reveal his secrets and hidden thoughts to him just as he reveals them to himself, because this person is not distinct from himself, and it is fitting that he love him as he loves himself. This is as the Torah states, “You shall love your fellow as yourself” (Leviticus 19:18), i.e., just as your love for yourself involves no other, so too, with regard to your love for your fellow, you should not think of him as being distinct from you, as the definition of absolute love is that the lover and the beloved become one. This is why the numerical value of the word love [ahava, which is thirteen], is the same as that of the word one [eĥad]; for the beloved is not separate from the lover at all. (Rav Yosef Albo, Sefer HaIkkarim 4:45)

Further reading: For a discussion of whether one’s life takes precedence over the life of another person, see A Concise Guide to the Sages, p. 162.