Before Dario Argento, there was another Italian maestro of horror named Mario Bava. Black Sunday was his directorial debut, and he would go on to influence a number of genres other than horror (the fantastic Diabolik was possibly the first film to bring an adult sensibility to comic book movies).
It was also the first major film for the iconic Gothic goddess Barbara Steele (pictured above). She plays a dual role in this - the vampire-witch Asa and her descendant Katia. Asa spends much of the movie lying in her crypt, causing all kinds of hell to break loose just with her mind. But Steele's performance, both as the wicked Asa and the virtuous Katia, is something to behold, especially for a first starring role.
This reminds me a lot of the story of Dracula, and perhaps that is more than incidental, since Francis Ford Coppola borrowed several set-pieces directly from this film for his Dracula film. But there are other similarities, such as the villain doing most of their nefarious deeds through others while they are too weakened to do much themselves.
Several of the elements of vampire lore are here. Asa's coffin has a window, over which sits a cross - to keep her from getting up and causing trouble. She has to be destroyed by fire. And of course she is dependent on blood. On the other hand, we're not shown she has any aversion to sunlight or garlic, and she doesn't seem to have the ability (or perhaps she just lacks the inclination) to turn other people into vampires.
If you ask people about this movie, the thing that will most likely leap to mind is the opening scene. Asa is about to be burned at the stake, but before that, she is branded and has a mask placed on her face. Not just any mask, The Mask of Satan, which has metal spikes all up on the inside. They place it on her face and lodge it into place with a huge hammer. Later edits of this movie would cut out the shot where blood spews out of the mask when the hammer meets it. Pretty intense stuff for 1960, as were many other gory (for the time) scenes in the film, and it was even banned in the UK for a long time. One critic wrote of the movie at the time "As a setting for unadulterated horror, it will leave its audiences yearning for that quiet, sunny little motel in Psycho."
I think that's a compliment, whether it was intended as such or not. The whole movie is on YouTube, if you're interested, but here's a little taste, along with some commentary by some well-known horror fans.