brotherly love: the warm, loyal affection fellow believers owe one another as brothers and sisters in one family
In everyday Greek this word named the affection between people born of the same mother, real brothers and sisters. Every writer from the old playwrights to Plutarch used it that way, and kings even took it as a title to show off their family loyalty. The New Testament does something startling with it: it keeps the word but changes who the brothers and sisters are.
Here the word always means love among fellow Christians, pictured as siblings in one household whose Father is God. The writers never argue for this; they simply assume it. Paul can tell a church he has never visited to keep it up (Romans 12:10), and Hebrews can plead "let brotherly love continue" (Hebrews 13:1) to a community under real pressure. The bond is meant to be as strong as blood kinship, or stronger.
This is not a lesser or softer love than the wide, self-giving love the New Testament calls ἀγάπη. The two differ in reach, not in depth: ἀγάπη is love flung wide, even toward enemies, while this word aims that same love at its home inside the family of faith. Second Peter sets them in a single climbing chain, family affection opening out into love for all (2 Peter 1:7).