From the site:
The Nāgarī or Devanāgarī alphabet descended from the Brahmi script sometime around the 11th century AD. It was originally developed to write Sanksrit but was later adapted to write many other languages.
The name Devanāgarī is made up of two Sanskrit words: deva, which means god, brahman or celestial, and nāgarī, which means city. The name is variously translated as "script of the city", "heavenly/sacred script of the city" or "[script of the] city of the Gods or priests". The origins and meaning of the name are uncertain.