Refrigerators cool things down by taking advantage of the way substances absorb and unload heat as their pressure points and phases of matter change (usually from gas to liquid and back). It's difficult to pinpoint a single inventor of the refrigerator, because the concept was widely known and gradually improved over the course of about 200 years. Some credit Oliver Evans' 1805 unproduced design of a vapor-compression unit, while others point to Carl von Linde's 1876 design as the actual precursor of the modern refrigerator in your kitchen. Dozens of inventors, including Albert Einstein, would refine or improve refrigerator designs over the decades.
In the early 20th century, harvested natural ice was still common, but large industries such as breweries were beginning to use ice-making machines. Harvested ice for industrial use was rare by World War I. However, it wasn't until the development of safer refrigerant chemicals in the 1920s that home refrigerators became the norm.
The ability to keep food cold for prolonged periods (and even during shipping, once refrigerated trucks were developed) drastically changed the food production industry and the eating habits of people around the world. Now, we have easy access to fresh meats and dairy products even in the hottest summer months, and we're no longer tied to the expense of harvesting and shipping natural ice -- which never could have kept pace with the world's growing population in any case.