North American domestic power supplies are typically derived from a centre-tapped transformer with the centre tap acting as neutral (required to be grounded (earthed) in the home distribution panel (aka fuse box)). The two outer taps are each at a potential of 120 volts to the neutral, but being derived from a single transformer secondary winding are at a potential of 240 volts to each other.
Larger appliances such as stoves are connected across these two 120 volt lines and so run at 240 volts. Due to the construction of household distribution panels, alternate circuit breakers are on alternate 120 volt lines. By using adjacent circuit breakers which are mechanically linked, a 240 volt supply is available. 240 volt rated outlets (sockets) are easily available and have a different configuration to 120 volt outlets.
For many years I have used one of these 'combined' 240 volt outlets to power old UK tools. Note that both hot wires are at 120 volts to ground (earth) and both are protected by a circuit breaker - in my case 20 amps. A short circuit between either hot wire and ground will trip its respective breaker.
Now to the device shown. As distribution panels have alternate connections to one or other of the 120 volt lines it is possible to plug this device into outlets (sockets) coming from two different hot lines and thus provide 240 volts at its combined socket.
Although a change in rules has recently occurred, most kitchen outlets (they are known as duplex, having two outlets in one box) are wired separately with each one on a different 120 volt hot line. The wiring between the distribution panel and this 'combo' outlet uses a three wire + ground cable, with a single neutral wire going to both outlets and the other two wires going to the two different 120 volt hot sides.
This device could be plugged into one of these 'combo' outlets so providing 240 volts for some European or UK 240 volt devices.
This arrangement is not inherently dangerous. Of course the wiring in this device must be suitable for the load current of the 240 volt device.
If someone mistakenly plugs both 120 volt plugs into circuits derived from the same 120 volt hot line, the combined outlet will have a zero voltage across it instead of 240 volts, although both will be at 120 volts compared to ground. There remains the possibilty that an outlet has been incorrectly wired with hot and neutral reversed. In that case plugging the second plug into an outlet will result in a loud bang, possibly some smoke and one of the circuit breakers will have tripped. A simple North American outlet tester 'available at all good hardware stores' will confirm correct connections.
The device is likely not approved for use in North America and I have no idea if approval could even be obtained. Just on the lack of an official stamp of approval, I would suggest that the device should not be used.
Your alternative, if you really need 240 volts, is to get a licensed electrician to install a 240 volt outlet. You will need two spare, adjacent slots on the distribution panel and the circuit breakers must be the mechanically linked design. The device will need a new North American 240 volt plug, available from larger hardware stores.
A footnote: North America uses a different AC frequency to Europe/UK which may affect some devices. For example record players used the mains frequency to set the speed, so do not 'cross the pond' easily. An alternative is a single phase converter, which can derive 240 volts from 120 volts at the correct frequency for the device and without any special wiring.