Why is it that when holding a hose horizontally and water flows from the end of the hose then twisting the nozzle of the hose to partially closed causes the water to shoot farther from the end?

Closing a hose nozzle makes the opening smaller. The same amount of water tries to flow though a smaller area. It is like a bunch of people trying to go through a door at the same time. The only way they all can get through in the same time is if they all line up and walk faster. That smaller opening causes an increase in the speed of the water (higher velocity). Because the water is moving faster, it travels farther before the natural force of gravity causes it to fall to the ground.