I have read that the Buddha said the cause of suffering is ignorance of the "nature of reality". Is this correct?
Coming into existence or 'birthing' (jati) is the cause of suffering (dukkha). Dependent Arising - Paticca samuppāda by Piya Tan
What is the "nature of reality" that the Buddha talks about?
All conditioned things (forms, verbalization, mental thoughts), are forever changing (anicca), lead to suffering (dukka), and devoid of a permanent entity/owner (anattma). Read about the Tilakkhana or the Three Characteristics in the Dhamma.
may you be happy.