We know in a time-span of 24 hours there are altered sessions of day and night. Certain part of the world illuminates when it faces the bright Sun and the rest of the part sleeps in dark during the moment. Though the darker side is also not completely dark all the times in a month as it manages to get some lumen from the moon. Think for a possibility that if there is a star in the Universe which is probably brighter than the sun and can throw its rays to darker part of the earth and lighten the earth? Now you will say that the star would be billion light years far so it may take billions of years for this event to happen. It may be partly true but we can't reject the fact that the said star may on its way to complete its cycle might be nearing earth so the light may reach the earth in lesser billion years as assumed before. Well,this is one school of thought.
Now think if there is a star which is not a emitter of light but bigger in size than the star in the picture and it is right now blocking the path of the light emitting star. So, whenever this bigger star while moving unblocks the view of the illuminated star from the earth then the chances are there that the darker side of the earth which is not illuminated by the sun rays may get illumination from that particular star. And probably the lumen reaching the earth may be more than the lumen received from the sun so it can be concluded that the night can be brighter than the Day!