Maraging steel (or 'high maraging steel') is a particular type of steel alloy. Generally, it is known for being very strong at room temperature without being as brittle or hard as steel strengthened with additives such as chromium and for having very little or no carbon content. The word maraging is actually a portmanteau, and is constructed from martensitic and aging. Aging, here, doesn't refer to the sort of process used to make good wine or tasty steaks; rather, it refers to the length of the cooling period as the steel is forged. The higher the maraging, the longer the cooling period has been artificially extended. This tempers the steel as it cools, and increases its strength and resistance to cracking.
To make maraging steel, iron is alloyed with another metal - usually chromium (for stainless variants), cobalt or nickel. Allowed to cool, this alloy produces martensite, a brittle but strong crystalline structure. However, when cooled more slowly than normal heat transfer would proceed, usually by managing the environmental temperature and letting it drop more slowly than the metal would cool on its own, causes the resultant steel to retain a lot more ductility than it otherwise would, which makes it more desirable - in addition to the structural strength provided by the martensite crystal structure, the alloy remains ductile enough to resist cracking and fracture very well. As a result, it is used in the most extreme environments, such as rocket motor casings and aerospace components in general, where a combination of heat and vibration and stress are all present. The higher the maraging, the longer its cooling has been artificially extended. It is difficult to keep conditions appropriate for this process for long periods of time, and takes more energy to maintain an environment hot enough to match cooling liquid steel - so of course it's more expensive.
Clockmaker notes: "For the record and hopefully of some small interest, maraging steel is also the standard in sport fencing swords, ever since Smirnov died from a snapped blade through the eye in '82."