There's one key understanding that is necessary for this story to make sense: martyrdom is a desirable thing. Once you accept the idea that dying for your faith is a ticket to salvation, the rest of the story falls into place. Without that, it wouldn't make any sense at all.
Nicephorus and his friend Sapricius had a spat. Well, more than a spat. Something passed between them which Sapricius found unpardonable. Repeated efforts by Nicephorus to reconcile were rejected.
Then the persecution of Valerian and Gallienus rolled around. Sapricius, lucky bastard that he was, had the good fortune to get busted. Naturally he declined to make sacrifices to the Roman gods and was sentenced to be beheaded. Nicephorus heard about the impending execution and intercepted the squad assigned to march Sapricius to the execution grounds. He flung himself on the ground in front of his former friend and begged his forgiveness, but once more, Sapricius hardened his heart against Nicephorus.
And that's when his good luck turned. In rejecting Nicephorus, he rejected turning the other cheek, loving your neighbor as yourself, mercy and kindness and all that stuff. He rejected Christ. His will faltered and he found himself asking the guards for permission to sacrifice to the pantheon and spare himself. They immediately obliged.
Of course, they couldn't help noticing Nicephorus groveling in the dust. They would have been guilty of gross negligence of duty if they did not at least inquire about his religious disposition. Naturally, Nicephorus confessed himself Christian. The guards roughed him and they cuffed him and took him off to the execution grounds where he promptly claimed the crown of martyrdom that had nearly belonged to Sapricius.