Brotherly love in the biblical sense is an extension of the natural affection associated with near kin, toward the greater community of fellow believers, that goes beyond the mere duty in to "love thy neighbour as thyself", and shows itself as "unfeigned love" from a "pure heart", that extends an unconditional hand of friendship that loves when not loved back, that gives without getting, and that ever looks for what is best in others.
The following is based on the public domain article Brotherly Love found in the 1906 Jewish Encyclopedia
Brotherly love is the love for one's fellow-man as a brother. The expression is taken from the Greek word Φιλαδελφία (Philadelphia = "love of brothers"), which trait distinguished the Early Christian communities. Romans.12:10;1Thessalonians.4:9;John.13:35 – 1John.2:9;3:12;4:7;5:1 and 1Peter.3:8;5:9 express the idea of Christian fellowship and fraternity. It was also important in the Essene brotherhoods, who practised brotherly love as a special virtue. Brotherly love is commanded as a universal principle in : "Thou shalt love thy neighbor as thyself," the preceding verse containing the words: "Thou shalt not hate thy brother in thine heart." This commandment of love, with the preceding sentence, "Thou shalt not avenge nor bear any grudge against the children of thy people," may originally have referred, and has by some scholars been exclusively referred, to the Israelitish neighbor; but in verse 34 of the same chapter it is extended to "the stranger that dwelleth with you . . . and thou shalt love him as thyself." In it is declared unjust to wrong the servant in his cause: "Did not he that made me in the womb make him? and did not one fashion us in the womb?"
A friend loveth at all times, and a brother is born for adversity.
The principle of brotherly love, including all men, is plainly stated in the Book of Wisdom i. 6, vii. 23, xii. 19: "Wisdom is man-loving" (Φιλάνθρωπον); "the righteous must be man-loving." The Testaments of the Patriarchs teach the love of God and love of all men "as [His?] children." Commenting upon the command to love the neighbor (Lev. l.c.) is a discussion recorded between Rabbi Akiva, who declared this verse in Leviticus to contain the great principle of the Law ("Kelal gadol ba-Torah"), and Ben Azzai, who pointed to Gen. v. 1 ("This is the book of the generations of Adam; in the day that God created man, in the likeness of God made he him"), as the verse expressing the leading principle of the Law, obviously because the first verse gives to the term "neighbor" its unmistakable meaning as including all men as being sons of Adam, made in the image of God. Tanhuma, in Gen. R. l.c., explains it thus: "If thou despisest any man, thou despisest God who made man in His image."