How did he die..........?

I was wondering, I thought that Naz Gul couldn't die...How did Eoywn kill him(granted I know Pipin did stab him w/ his own blade, but was that the only way to kill it, and why is it painful to him when he stabs the Naz Gul with the blade) Or was it just that the Naz Gul meant it literally when he said that "no man could kill him" and that only a women could? Does anyone know the answer