Manufacturing engineering programs prepare people to plan and build systems used to produce goods. Students learn about tools, production techniques, and how computers are used in production. They also learn to use math and science to solve real-life problems in system design.
Think about the last really nice manufactured gift you got (other than jewelry). Now imagine how much it would be worth if it were melted down to its raw materials. Not much, right? The difference in value is largely due to manufacturing engineering.
Manufacturing engineers find ways to make a few pennies' worth of raw materials into something worth a whole lot more. They design manufacturing processes and the systems that get those processes done. They perfect those systems so that the finished goods are affordable. For example, they may use robots to save on the costs of human labor.
When you study manufacturing engineering, you start with a good helping of science and math. You study energy and the properties of materials. Then you learn how to solve engineering problems using the scientific method.
Manufacturing operations can be very complex, so you learn how to break a problem down into its parts. You learn how to design experiments or simulations to test various ways of improving each part of the operation.
After four or possibly five years of full-time study beyond high school, you should be able to earn a bachelor's degree in this field. This is good preparation for entry into your first job. Only a handful of colleges offer a bachelor's degree in this specific field.
Another route is to do your bachelor's in mechanical or industrial engineering. Then get a master's degree in manufacturing engineering. This usually takes one or two years beyond the bachelor's. Over 50 graduate schools of engineering in the U.S. offer this program.