“Liquid air” means air – the stuff you’re breathing right now – chilled and stored in a liquid form at -256 degrees Farenheit. When it’s injected into the engine along with a room-temperature heat-exchange fluid (which won’t freeze in the engine), the liquid air boils – it turns into a gas, creating a lot of pressure and powering the engine.
The “pros” of this idea (compared to hydrogen, at least, which is the other volatile gaseous fuel being considered as an alternative to hydrocarbons) are that A) industry already produces liquid gases in huge quantities, B) there’s already well-established distribution infrastructure for it, C) it’s easier to store than hydrogen, and D) there’s much less of a chance for it to explode.
There are still big hurdles for the tech, if it wants serious consideration. First, we need to know how much energy it takes to liquify air, transport it, and then use it in a car engine – the stuff is a way to store energy in liquid form, so the efficiency of the process is important. Storage is also a problem – liquid air evaporates even under pressure and while insulated, so if you leave your car alone with a full tank of “gas,” and come back after a month, you might find it’s emptied. That might be a bit of a problem. And let’s not forget that it’s still a gas (in liquid form, admittedly) being held under pressure – it will go “pop” under the right (wrong?) conditions, and is quite capable of creating a burst of shrapnel.
TL;DR – cool idea, don’t know if it’ll work.