What does it mean?
Non-returner. A person who has abandoned the five lower fetters that bind the mind to the cycle of rebirth (see saṃyojana), and who after death will appear in one of the Brahma worlds called the Pure Abodes, there to attain nibbāna, never again to return to this world.
-from Access to Insight
Why does it matter?
Here’s a topic that doesn’t come up too often in Intro to Buddhism courses down at the local meditation center!
One of the tenants of Pure Land Buddhism is that Buddhism has degenerated to the point that it is no longer possible for ordinary people to hope to become enlightened. Our best shot is being reborn in a heavenly realm, where the future Buddha Amitaba can teach us directly and lead us to enlightenment. From the Theravada perspective it sounds a little looney, but the seeds of that idea are right there in the early texts.
The Buddha taught a Gradual Training, and part of that gradual training was a series of accomplishments that one could attain leading to enlightenment: Sotāpanna, Sakadāgāmī, Anāgāmī and Arahat.
An ordinary person is a pathujjana. This includes everyone from mass murderers up through dedicated Buddhists that still struggle with doubt.
Sotāpanna is Stream Entry, the first stage.Stream Entry is actually no small thing. It means that someone now has total faith in the Buddhist practice, and will never fall away from the practice, no matter how often they are reborn. The great Buddhist scholar Buddhaghosa ended his magisterial commentary the Visuddhimagga by wishing that it would help lead him to Stream Entry! It also means that one will be reborn at most 7 times, and each rebirth will be either as a human or in heaven.
The next stage, Sakadāgāmī, means that a person will reborn at most once as a human, though they might be reborn again in heaven. Anāgāmīs can only be reborn in heaven, the Pure Abodes. They will never be reborn as a human or lower. Anathapindika was a famous Anāgāmī. And Arahat is of course a fully enlightened being, with enlightenment equal to the Buddha himself.
Here’s a question that is sometimes batted around by people interested in this kind of thing: Did the Buddha go through this progression, or just jump right to arahat?