Dr Mortimer says this as Sir Charles apparently foresaw the manner of his death by means of a supposedly spectral hound. The means of his death appears therefore to have been highly unusual, but fits in with the old manuscript that he gave to Dr Mortimer, which relates the story of the hound that is meant to haunt the Baskerville family. This is the 'document' that Mortimer says Sir Charles 'took very seriously' (chapter 2).
However, Mortimer declares that Sir Charles was not superstitious to begin with.
He was a strong-minded man ... shrewd, practical, and as unimaginative as I am myself. (chapter 2)
Yet Sir Charles became increasingly nervous in the months leading up to his death, due to glimpses of a huge beast around the Baskerville residence out on the lonely moors. This led him to believe in the existence of the Baskerville phantom, and therefore, as Holmes eventually deduces, he was literally frightened to death by the apparition of a large, glowing hound at his gate.
However, Sir Charles did not realise that this fearsome creature was not a phantom but a real dog, used by his villainous neighbour and unsuspected cousin Stapleton in an attempt to gain control of the Baskerville estate.