Original: However, a gene that prompts behaviour which enhances the fitness of relatives but lowers that of the individual displaying the behavior, may nonetheless increase in frequency, because relatives often carry the same gene; this is the fundamental principle behind the theory of kin selection.
Simplified: However, a gene that prompts behaviour which enhances the fitness of relatives but lowers that of the individual displaying the behavior, may nonetheless increase in frequency -  relatives often carry the same gene, after all.