Galaxia is a possible future state for the human race in which all planets, all humans, all life, and even non-living organic matter would be incorporated into one single organism. Galaxia is an alternative to the Second Galactic Empire that the Seldon Plan is trying to achieve.
When Isaac Asimov decided to link the Foundation series to the Robot series there were profound implications for galactic civilization not touched upon in the original Foundation trilogy. In particular, R. Daneel Olivaw, a telepathic robot, was secretly manipulating humanity according to the dictates of the Laws Of Robotics. Daneel had also adopted the Zeroth Law of Robotics which says, "A robot may not harm humanity, or, by inaction, allow humanity to come to harm". The Zeroth Law was a problem for Daneel because it was too difficult to know what best serves the interests of humanity. Daneel found it necessary to try to shape humanity into a more easily understood phenomenon, a type of collective super-organism with a single more unified group mind. This fantastic project, growing ever more complex as humans spread through the entire galaxy, stretched over 20,000 years.....the ultimate goal was Galaxia.
If every human in the galaxy could become part of a single "organism", Galaxia, then Daneel would find it much easier to judge how to follow the Zeroth Law and keep humanity from harm. Working towards that goal, Daneel first had to create Gaia, an entire planet that could serve as an experimental prototype for the kind of trans-galactic group mind that was the ultimate goal. A key part of creating the Gaia super-organism was how to make humans give up their individuality and accept a role within the Gaia collective. In order to accomplish that, Daneel had to (genetically?) engineer humans so as to give them a set of innate behaviors similar to the Laws Of Robotics. According to Daneel (at the end of Foundation and Earth) a key part of this fundamental change to human nature was the need to make a (genetically modified?) type of human who would value life as a whole more than their own selfish needs.
However, even that fundamental change to human nature was not enough for Daneel. With all of Daneel's claimed worries over making the wrong decisions about how to protect humanity, Daneel decided to also endow the humans of Gaia with telepathic abilities similar to his own. This was required in order to make Gaia a single organism with a group mind that could be understood according to the Laws Of Robotics.
At the end of Foundation and Earth Daneel's great plan is nearing completion after 20,000 years of effort. However, one problem remains: Daneel is dying. In order to have time to complete the formation of Galaxia, Daneel must merge his memories into the mind of a humanios, Fallom. Clearly, such a process would be a major technological achievement, but just another subtask for Daneel's 20,000 year long Galaxia project. This ability suggests the possibility that it may not have been necessary to genetically modify humans in order to give them an "innate" respect for life that was stronger than the instinct for individualism and independence. Maybe Daneel found a way to impress robotic behavioral patterns on humans by way of a type of partial mind transfer.
In 498 F.E., councilman Golan Trevize and historian Janov Pelorat are maneuvered to Gaia so Trevize can decide whether the future of the Galaxy is to be guided by the First Foundation, Second Foundation, or Gaia. Trevize has the unique ability to deduce the correct solution to a problem, even with little or no information on the nature of problem itself. Trevize chooses Gaia, therefore Galaxia, because R. Daneel Olivaw could not proceed with Galaxia for risk of harming humanity in the process. The creation of Galaxia would provide a better defense of humanity against aliens from other galaxies.