When Makoto Yuki is recruited to S.E.E.S. in April, Shuji Ikutsuki and Mitsuru Kirijo explain their understanding of Shadows and Apathy Syndrome to him. Shadows are beings that appear during the Dark Hour. In the event a normal person not transmogrified into a coffin during the Dark Hour, then they are likely to be attacked by a Shadow. The Shadows eat the minds of their victims, resulting in the victim becoming unable to speak or move. This condition is known as Apathy Syndrome, and those who have contracted it are called The Lost. If left to their own devices, they will perish due to malnutrition or accidents. Thus, one of S.E.E.S.' goals is to defeat Shadows and prevent more ordinary people from becoming The Lost.
It is later revealed that Ikutsuki was manipulating S.E.E.S. into defeating the Shadows that appeared during Full Moon operations so that they would recombine into Death.
During Story Mode, Naoto Shirogane says the true cause of Apathy Syndrome was when a Shadow left its owners body. Naoto believes the coma victims in Dancing All Night are similar to the victims of Apathy Syndrome. Except this time around, the Shadows are being forcibly removed from their owners, and the Investigation Team being able to wield their Shadows as Personas has prevented them from falling into the Apathy Syndrome-like coma.
In the Persona 3 lore and setting book, Persona Club P3, it is clarified that Shadows do not actually eat humans. The real cause of Apathy Syndrome is when a human loses the will to live and their Shadow leaves them. Shadows originated from Nyx but now exist as part of human minds, and being without their Shadow makes humans non-functional thus giving the appearance of what is called Apathy Syndrome. Defeating Shadows causes them to return to their respective humans and cures them of Apathy Syndrome.[1]
Despite the name, Apathy Syndrome is more akin to akinetic mutism than it is to apathy, mainly that akinetic mutism is the tendency to not move or speak due to diminished motivation while apathy tends to only hinder emotional stimulation and decrease productivity.