This line comes at the end of the novel, as the narrator thinks back on the invasion and on the first time he saw a Martian craft, crash-landed in the dirt.
And strange, too, it is to stand on Primrose Hill... to see the sight-seers about the Martian machine that stands there still, to hear the tumult of playing children, and to recall the time when I saw it all bright and clear-cut, hard and silent, under the dawn of that last great day....
(Wells, The War of the Worlds, eNotes eText)
While the day of the Martian arrival cannot be thought of as a "great" (positive) day, it can be thought of as the last day that Humanity was alone and living in relative peace. In that sense, the day was great because it preceded the War and the deaths of so many people; it was also objectively "great" (extraordinary) because it was the first contact between humans and aliens. In the context of the novel, the day was "great" but not "good," and so his reference is poetic and not literal.
The narrator refers to the day the Martians landed as the "last great day" at the end of the book, even after the Martian invaders have died. The narrator is referring to the good times that took place before the death and destruction that the Martians wreaked on earth, with their black smoke and heat rays.
The narrator also feels that "the stress and danger of the time have left an abiding sense of doubt and insecurity in my mind." Even though life has resumed its normal patterns, he has a sense of foreboding about the future. He thinks about the Martians, "To them, and not to us, perhaps, is the future ordained." In other words, he fears that the Martians' offensive on earth is only the first among many efforts that the Martians will lead towards destruction and death in the solar system. The narrator also cannot escape the trauma of the past. At night, he sees "the black powder darkening the silent streets, and the contorted bodies shrouded in that layer." The trauma of living through the Martian invasion has not left him, and it is not likely to ever go away.