When oxygen is in a cold state ( -183ºC), it turns to liquid. More oxygen molecules fit into the same space when in liquid form compared to when it is a gas and so liquid gas only takes up 10% of the space that compressed oxygen does. Therefore this liquid allows for a greater amount of oxygen to be placed in a tank and it weighs less than a compressed oxygen tank.
Liquid oxygen is stored in an insulated stainless steel low pressure container that works in a similar way to a Thermos flask. These base units store and hold the liquid oxygen at an extremely low temperature. As with the compressed oxygen, it can be filled into smaller units from the base unit so that it can be used portably.
Liquid oxygen doesn’t require power via electricity like oxygen concentrators do and also they make no noise.
There are some disadvantages in that liquid oxygen is more expensive than compressed oxygen and does not have as long of a shelf life as it will evaporate over time. Also, you will not be able to take liquid oxygen on a plane.
References: http://www.uk.airliquide.com and http://www.inogen.com