The notion that arousal or excitement induces bloody noses (hanaji or "鼻血") isn't just part of anime or manga iconography. It's also become an old wives' tale of sorts. But is it true?
According to Dr. Kouichirou Kanaya, "The notion that sexual arousal causes the heart rate and blood pressure to rise is something that's a well documented fact; however, in actuality, sexual arousal and bloody noses have no direct connection."
Bleeding in the front of the nasal septum often causes nosebleeds. In the case of kids, picking might cause bloody noses. There's a whole host of other reasons that can cause bloody noses that range from dry air to cocaine use and from allergies to hemophilia—and more (the Mayo Clinic has a much more detailed list).
"Bloody noses," the doctor adds, "are probably used to show in a powerful way just how excessively large the change induced by sexual arousal is." It's a climax, and in manga, it often seems to be code for ejaculation.
The trope is very much a Japanese one, appearing throughout the country's popular culture and with various nuances in anime and manga. It is not a new trope and has existed for years.
Manga artist Yasuji Tanioka is believed to be the first one to introduce the motif with his early 1970s manga Yasuji no Mettameta Gaki Dou Kouza. Other manga artists liked the expression and began replicating it in their own work.
While sexual arousal induced nosebleeds don't seem to be backed by medical science, they have become shorthand for stimulation. If they've made it this many decades, don't expect the bleeding to stop any time soon.