Minicomputers were introduced in the 60s as smaller, less expensive alternatives to room sized mainframes. They were closer to a refrigerator or mini fridge in size and sometimes could be carted around on casters. One could even fit in the back of a Volkswagon at the time.
Examples are the DEC PDP-8 and Data General Nova. This article covers the definition of the term "minicomputer" and attempts to classify the first machines.