Change from day to night happens because the Earth rotates on an axis. Every young student today knows this, but people are so used to it that they rarely think of the importance of this simple motion. Should it ever stop, the consequences will be disastrous for all life.
The first consequence of stopping the Earth’s rotation is a great shift in everything. Think of the fact that the planet is constantly on the move. This means that its rotational velocity, although unnoticed by people, is rather high. Putting an abrupt stop to the movement will make everything on the surface of the planet move extremely fast, the strongest impact felt at the equator. This is an immensely catastrophic idea, because the oceans that will shift due to this momentum have the power to wipe out almost all life on Earth.
The distinction between day and night will cease to exist. There will always be daytime on the half of the planet that is turned towards the sun; there will always be night on the other. Messing up your biological clock is one of the smallest problems this change will cause, as many species will simply die out because they cannot adapt to such a profound change in their biorhythm. People are more adaptable, but they will need to create alternative means of food production. Not many vegetables can grow without a shred of sunlight. Providing artificial lighting will have to address the problem of resource depletion.
Another serious problem that people will face is a dramatic change of weather. It will take some time, but the half of the planet that is turned towards the sun will eventually start to burn. It will turn into a massive desert, and will continue to heat up until surviving there becomes completely impossible. The other half of the planet will be attacked by cold and will eventually suffer the same fate. Unless humans manage to evolve and change their bodies to survive in this new rough environment, they will die out and leave the world clear for other species.
Remember that stopping the rotation of the Earth is impossible, so the horrors of these consequences that we might have to face should not panic you. However, they do need to be studied. This will emphasize the importance of a responsible approach to progress, and ensure that scientists consider everything they do much more thoroughly.