You're talking about a senter jack, so that you lift the bike in one go? Or..?
Not really sure what you call it. I always just called it a motorcycle/ATV lift. It has four wheels, two of which are swivel casters. It has two horizontal arms that go under the bike frame between the wheels, along with connecting linkages that keep them horizontal as they are lifted by a hydraulic jack that is foot pedal operated. It has a removable handle that allows you to pull or push it around wherever you want it after you lift the bike.
Some bikes like the Rebel 250 require blocks between the bike frame and the jack arms to prevent lifting on the exhaust pipes or mufflers. Others like my Harley's which have the frame below the exhaust just sit directly on the arms. The arms have a rubber pad so the bike won't slip. There are loops provided on the arms, and I usually use ratchet straps on each side to attach the bike securely to the arms. This allows you to work on the bike, pull wrenches, push on it, sit on it, etc. without worrying about it falling off the jack or tipping over. It is not completely necessary as the bike usually balances and sits on it pretty solidly, but it is just a safety measure for a little more confidence. With it strapped on, it would be hard to tip it over if you and a buddy tried.
I use it for oil changes, tire work, chain service, winter storage, or anytime I want the bike lifted or stabilized to make it easier to work on. It will raise the bike about 18" if needed, or just barely clear the floor, or just decompress the suspension, or anywhere in between, depending on what you are doing to it.