A minicomputer isn't very mini. At least, not in the way most of us think of mini. You know how big your personal computer is and its related family. A workstation is the next step up in size, performance, and price, and is similar to a personal computer in that it is used by one individual.
Then comes the minicomputer. A minicomputer costs from $20,000 to $200,000 or so. It is built to perform different tasks for different people at the same time. Each person using a minicomputer has their own terminal attached by wires or via a modem to the computer proper. (A terminal isn't a computer-it's basically just a keyboard and a monitor; see the full definition.) The minicomputer spends a little bit of time on one person's task, then moves on to the next, and so on, juggling the work based on which jobs it thinks are most important. If you're the only one using a minicomputer, this can be one fast machine.
But once many users (people) are "on" the system, the thing begins to slow down-you may type something and then wait for a minute or more before you see a response on the screen. Minicomputers used to be the only option for companies. Now, many firms are turning to networks of personal computers to accomplish the same thing faster and cheaper.