It's not uncommon for there to be day and night in open-world games, but usually day is bright and sunny, night is dark, and that's all there is to it. This isn't the case in Dying Light--when the sun goes down, everything changes. In the demo, the character was finally able to find a supply drop (besides the first one, which was guarded by gun-toting soldiers), but he arrived just as the sun went down.
During the night, the zombies behave more aggressively. This, alone, is disconcerting, but even more troubling is the other stuff that shows up when it's dark out. There's a different, mysterious kind of monster that prowls the streets after dark, hunting down the living (instead of, you know, just wandering around like a dumb zombie). You can try to outrun them, hide from them, or avoid them altogether by getting back to your base before they arrive.