More modernly it just means you swear to do something no matter what, and since it's a blood oath, modernly it means hurting or even killing others in oath, thus 'blood' oath, meaning blood would be shed in promise to the task, usually a phrase only used by mobsters and crooks.
The Prince and his loyal Knight cut their palms and then shook hands, promising each other in a blood oath they'd never split apart.
Officer Eliot of the Chicago PD & Officer Hunter of the Seattle PD made a blood oath that whatever happens, they will stop crime in their city, willing to do whatever it takes to keep this oath.
Kingpin Chuck Norris told a footman of his black market empire that if he did not go through with the hit, he'd kill his family. The footman then made a blood oath, swearing he would.