SIM-free means you can put your own SIM in, so you are not tied to their provider. If, for example, you buy a SIM phone from Tesco you might find that it is tied to their network; they are usually cheaper because they're getting your network custom as well as the profit on the phone. Even with a SIM phone you can keep your old number but you will have to switch to their network.
The non-SIM phone sits in your home and connects to the standard telephone network. Usually BT. Can be wireless these days, but was traditionally cabled. May even have a dial.