The Greek adjective basilikos means royal or kingly — belonging to or characteristic of a king. In John 4:46-54 it refers to a 'royal official' (a court official) whose son was healed by Jesus from a distance. In James 2:8 Paul describes the love commandment as the 'royal law' — the king's law that supersedes all others.
The 'royal official' in John 4 journeyed to Jesus in desperate need and believed Jesus' word before seeing any result — a pure model of faith. James calls the love commandment the 'royal law' (nomos basilikos) because it comes from the King of kings and sums up all human obligation. When we love our neighbors, we obey the King's supreme command. Law in Jesus' kingdom is not cold regulation but the warm pulse of love.