The Technological Singularity is the idea that in the (near) future an 'intelligence explosion' will happen, resulting in technological progress that's quicker than a ('non-enhanced', biological) human can understand.
Fundamental to the idea of the Singularity is the concept of 'Seed AI' or 'recursively self-improved AI'.
Seed AI is a hypothesized type of strong artificial intelligence capable of recursive self-improvement. If the AI was about as good at programming as the people that created it, it should be able to reprogram itself to be even more intelligent. Having improved itself it would then become better at improving itself, potentially leading to an exponential increase in intelligence.
Computers are already better than human intelligence in many ways. Your calculators can calculate quicker than you do, Wikipedia stores more information than your brain, computers can beat the best humans at chess, etcetera.
Humans still beat AI at things like pattern recognition and language. This isn't strange: the computational power of the human brain is only rivaled by the biggest and most expensive supercomputers. But if the exponential progress of computing power progresses like it has done for roughly the last century, affordable PCs will have the same power as the brain before 2030.
It seems likely that we'll figure out how the brain works (and use this to construct human-like AI) roughly around that year. Vernor Vinge expects the Singularity to happen before 2030, Kurzweil suggests 2045.
Human-like AI means that we can combine the best characteristics of human thinking and computers. You know in which ways you are 'superior' to computers, but there are many ways in which computers can improve upon human thinking...
Speed. Our axons carry signals at 75 meters per second or slower. A machine can pass signals along about 4 million times more quickly.
Computational resources. The brain’s size and neuron count is restrained by skull size, metabolism, and other factors. AIs could be built on the scale of buildings or cities or larger. When we can make circuits no smaller, we can just add more of them.
Rationality. As we explored earlier, human brains do nothing like optimal belief formation or goal achievement. Machines can be built from the ground up using (computable approximations of) optimal Bayesian decision networks, and indeed this is already a leading paradigm in artificial agent design.
Introspective access / editability. We humans have almost no introspective access to our cognitive algorithms, and cannot easily edit and improve them. Machines can already do this (see Eurisko and metaheuristics). A limited hack like the method of loci greatly improves human memory; machines can do this kind of thing in spades.
There is no reason in principle why machines could not surpass our abilities at technology design or general reasoning by a similar margin. The human level is a minor pit-stop on the way to the highest level of intelligence allowed by physics, and there is plenty of room above us.