Computing overhang refers to a situation where new algorithms can exploit existing computing power far more efficiently than before. This can happen if previously used algorithms have been suboptimal.
In the context of Artificial General Intelligence, this signifies a situation where it becomes possible to create AGIs that can be run using only a small fraction of the easily available hardware resources. This could lead to an intelligence explosion, or to a massive increase in the number of AGIs, as they could be easily copied to run on countless computers. This could make AGIs much more powerful than before, and present an existential risk.
In 2010, the President's Council of Advisors on Science and Technology reported on benchmark production planning model having become faster by a factor of 43 million between 1988 and 2003. Of this improvement, only a factor of roughly 1,000 was due to better hardware, while a factor of 43,000 came from algorithmic improvements. This clearly reflects a situation where new programming methods were able to use available computing power more efficiently.
As of today, enormous amounts of computing power is currently available in the form of supercomputers or distributed computing. Large AI projects can grow to fill these resources by using deeper and deeper search trees, such as high-powered chess programs, or by performing large amounts of parallel operations on extensive databases, such as IBM's Watson playing Jeopardy. While the extra depth and breadth are helpful, it is likely that a simple brute-force extension of techniques is not the optimal use of the available computing resources. This leaves the need for improvement on the side of algorithmic implementations, where most work is currently focused.
Though estimates of whole brain emulation place that level of computing power at least a decade away, it is very unlikely that the algorithms used by the human brain are the most computationally efficient for producing AI. This happens mainly because evolution had no insight, no deliberate plan in creating the human mind, and our intelligence didn't develop with the goal of eventually being modeled by AI. As Yudkoswky puts it, human intelligence, created by evolution, is characterized by this design signature - and it has developed poorly adapted to deliberation. On the other hand, when considering the design of complex systems where the designer - us - collaborates with the system being constructed, we are faced with a new signature and a different way to achieve AGI.