Someone who's faithless can't be trusted to be loyal. The faithless advisor to a king might turn out to be a traitor plotting against him.
If you're faithless, you're untrustworthy. You might be a faithless government worker, stealing state secrets to sell to an enemy, or a faithless boyfriend, secretly dating other people behind your girlfriend's back. The earliest meaning of faithless was "lacking religious faith," although it came to mean "deceptive" by the middle of the 14th century. Faith comes from the Latin fides, "trust, faith, or belief."