First of all they perform slightly different functions. The delete key erases text to the right of the cursor and the backspace key erases text to the left of the cursor. Also the delete key is capable of deleting icons, files, and folders. Pressing backspace when a file or other object is highlighted does nothing.
But the real reason why we have two keys that perform similar functions, is backward compatibility. Initially the computer keyboards replicated the typewriter keyboard which had a backspace function. New generation computer keyboards could not change the function of the original backspace key because people had already learned its behavior, so they had to add a new key. The behavior of the new key is more computer oriented and can be seen as an evolution of the backspace key.