(Adapted from the TranSocialist Alliance (http://transocialism.com) definition)
Transhumanist socialism is a particular type of socialism which holds that future transhumanist technologies such as nanotechnology will make it much more feasible to bring about a truly socialist world.
A transhumanist socialist believes that despite the risks that may be involved in these new technologies, such as even more potent weapons and means of totalitarian control, it is on balance worth developing transhuman technologies in the long term, because of their potential to transform society for the better. (Note that this in no way necessarily implies that technology alone can solve problems. Everybody must change as well, because true socialism is not just a matter of who is "in charge", it is a mode of being of a whole society, on a world scale and including every person.)
Thus being a transhumanist and being a socialist are both necessary but not sufficient conditions for being a transhumanist socialist. It is at least logically possible to be a socialist and a transhumanist without accepting the further idea that transhuman technologies will be of significant benefit in their efforts to create a more just world - or one may be a socialist and believe that future technology can alleviate some important problems with "the human condition", but it still doesn't make world socialism significantly more feasible than it already is. Neither of these positions fall within transhumanist socialism - they are merely transhumanist and socialist, which is quite different.
Of course, the word "socialism" can mean many things to many people. Its usage here needs to be clarified.
The term "Transhumanist socialism" was coined by Robin Green on March 6, 1999.
Transhumanists generally support present-day technologies such as genetic engineering (including of humans), cryonics, and advanced uses of computers and communications; as well as future technologies such as space travel, cloning and uploading of human minds into computer simulations.
Rather than believing that immortality can be achieved after death, Transhumanists strive for immortality by not dying; through the development of radically advanced health technologies and anti-aging medical practices, Transhumanists hope to establish an open-ended lifespan, to make death a purely voluntary decision.
Transhumanists may characterize their opposition as Luddites, and point to such notorious examples as Theodore Kaczynski, the Unabomber, who was convicted of sending parcel bombs to prominent people in key technology industries, killing three people and severely wounding two others.
Transhumanists generally support emerging technologies, including many that are controversial, such as nanotechnology, biotechnology, information technology, and cognitive science; as well as hypothetical future technologies such as artificial intelligence, mind uploading and cryonics.
As most transhumanists support non-technological changes to society, such as the spread of political liberty, and most critics of transhumanism support technological advances in areas such as communications and healthcare, the difference is often a matter of emphasis.
There are, however, a number of transhumanists that follow liberal forms of Eastern philosophical traditions, and a minority of transhumanists that have merged their beliefs with established religions (see Christian transhumanism).