* "niht" meaning "night"
* "mare" meaning "demon" or "evil spirit"
The "mare" part of the word was believed to be a creature that would sit on people's chests while they slept, causing them to have terrifying dreams or nightmarish experiences. This belief was widespread in Germanic folklore and is also reflected in other European languages, such as German "Albtraum" (alb = elf, traum = dream).
So, the word "nightmare" literally means "night demon" or "night evil spirit".