The Aldeans were a civilization native to Aldea, which was considered only a legend for thousands of years.
The society was self-contained and self-sustaining with incredible technical sophistication providing daily needs. Similar to cultural myths of Neinman on Xerxes VII or the Earth story of Atlantis, Aldea was said to have shed its past of violence and cultural conflict and evolved to a pure state, devoting themselves to culture and art. The Aldean culture developed by emphasizing the fundamental principle that for "everything taken, something must be returned." It was this principle that allowed their civilization to ascend to incredible heights in technology and art.
Having reached enlightenment, hundreds of centuries ago, the Aldean society retreated from the rest of the galaxy. To facilitate this, their progenitors built an enormous and advanced planet-wide defense system. The system, run by the computer called the Custodian, maintained an immense cloaking device and defense shield, in addition to a repulsor beam powerful enough to push starships several hundred light years away.
However, the long-term effects of the planet's defenses were extremely damaging. Millennia after the Aldeans retreated behind their cloak, cumulative wide-spread environmental damage, including depletion of their ozone layer, began to take their toll. The Aldeans suffered from long-term chromosomal damage from radiation poisoning due to exposure to their sun's ultraviolet rays. By 2364, the entire population of Aldea was infertile and depleted. No child had been born on Aldea for more than thirty years, and most of native wildlife on the planet, including all the fish in their oceans, had long ago become extinct.
Desperate to preserve their society as it would likely become extinct alongside themselves, the Aldeans, led by Radue contacted the USS Enterprise-D for help in repopulating their planet. Unable to reproduce themselves, the Aldeans offered to exchange their vast knowledge for a select few of the Enterprise-D's children. The Aldeans were physiologically very similar to Humans, which presumably was a deciding factor when they contacted the Enterprise-D. The Enterprise-D turned down the offer, leading the Aldeans to kidnap the children, creating a stand-off that was eventually resolved when Doctor Beverly Crusher proved that the very thing which had protected Aldea, its cloak, was responsible for their condition. Fortunately, Federation medicine would be able to reverse it and make the species fertile again.
The Aldeans returned the children and set about re-learning their own technology and adjusting to a new galaxy where they were no longer just a legend.
Aldean society was structured into units, or social groups, which specialized in a particular art or pursuit such as medicine or science. Within each group students were fully devoted to their discipline. The Aldeans had perfected their system of education and study to the point where the natural abilities of the individual blossomed very quickly, sometimes within hours or days of the student's first exposure to a medium. (TNG: "When The Bough Breaks")
According to RPG book Planetary Adventures, the Aldeans were split into several factions after the events of the episode. One faction, lead by Radue, favors joining the Federation. Another faction wants to ally with the Romulans. Yet another faction wants Aldea to remain isolated.