Columbo is a detective show that started in the 60s or 70s. It's kind of unique in that it's almost more from the murderers perspective. The first thing you see is the murder, which usually involved an elaborate plan to fake an alibi or hide evidence or frame someone else.

Despite their careful planning Colombo would always notice one little thing they missed and figure out who the killer is immediately. Then he would basically annoy them into slipping up. The criminal would become increasingly frustrated that this seemingly idiotic detective kept closing in on him. Colombo's signature move was letting the criminal thing they had tricked him with their explanation and leave. Then immediately pop back in saying "just one more thing" and ask them something that opened another hole in their story.

Death note is an anime about a highschool genius that finds a notebook owned by a "shinegami", a sort of Japanese grim reaper. He can kill anyone by writing their name in notebook. He becomes a vigilante and interpol hires a detective to catch him. Most of the show is a cat and mouse game between the two of them.

To kill someone with the deathnote you need to know their real name. It was a running joke that Colombo never said his first name during the whole series. Only people that have touched the death notes can see shinegami. This is the person Colombo is referring to at the end.