Dynamic class A has been around since the mid-1970s. Nelson Pass claims the invention of this idea (and holds a 1974 patent on it), the speaker power amps he designed during his tenure at Threshold Corporation used this scheme. Many Japanese companies then made copycat designs (Pioneer, Kenwood, Technics, Sansui, and others all introduced variations of the theme, and coined names such as "Non-switching", "New Class A", "Super A", etc.).
Clutz is correct in his description of how dynamic class A works. It has a adaptive output stage biasing circuit, which measures the output current and then in turn sets the output stage bias dynamically. At low output conditions, the biasing is kept low to keep the quiescent current low. As the output current demand increases, the bias is increased to prevent the amp from dropping into class AB (i.e., the output transistors are never allowed to switch off).
Obviously, dynamic class A solves a problem associated with "pure" or static class A designs; namely, the high constant current draw and hence requirement for a large power supply and output stage heatsinks. However, static class A has an advantage in that the high constant current flow through the output stage keeps the output transistors operating at a more linear region of its transfer curve, which reduces harmonic and intermodulation distortions. Dynamic class A does not possess this advantage. There are claims that dynamic class A's continuously changing bias leads to a form of dynamic distortion, although I have not seen concrete proof one way or another. It is worth noting that Nelson Pass has not used this technique in his own designs for some 25 years now -- he said that at reduced bias levels the sound quality is compromised.
For high power speaker amps, large power supplies (big transformers, filter caps, etc.), massive heatsinks and many paralleled pairs of output transistors constitute the bulk of the cost of the amp. Thus dynamic class A is more about cost-savings (and miniaturization) than about enhanced performance, especially in the 1970s-80's Japanese mid-fi products. And the "dynamic class A" aspect was used as a marketing jingle. This is not to say that dynamic class A is without technical merit -- it does avoid crossover distortion. Whether crossover distortion is the most significant evil in a particular amp is a whole different matter.
As jcx points out, for headphone amps, static class A power supply and heatsinking issues are scaled down to a much more manageable degree, so that (at least on mains-powered home amps) the complexity of a dynamic biasing circuit is not really justified.