The question is really just that - "What is stream"?
I've recently found this forum, and recently started reading some Buddhist scriptures, and I've seen the term a few times and have no understanding of it.
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Into the Stream -- A Study Guide on the First Stage of Awakening (by Thanissaro Bhikkhu) says,
The Pali Canon recognizes four levels of Awakening, the first of which is called stream entry. This gains its name from the fact that a person who has attained this level has entered the "stream" flowing inevitably to nibbana. He/she is guaranteed to achieve full awakening within seven lifetimes at most, and in the interim will not be reborn in any of the lower realms.
It includes the following definition,
The term "stream" in "stream entry" refers to the point where all eight factors of the noble eightfold path come together.
"Sariputta, 'The stream, the stream': thus it is said. And what, Sariputta, is the stream?"
"This noble eightfold path, lord, is the stream: right view, right resolve, right speech, right action, right livelihood, right effort, right mindfulness, right concentration."
"Very good, Sariputta! Very good! This noble eightfold path — right view, right resolve, right speech, right action, right livelihood, right effort, right mindfulness, right concentration — is the stream."
— SN 55.5
The coming-together of these factors is called the stream because it leads inevitably to two things, just as the current of a tributary will lead inevitably to a major river and then to the sea. In the immediate present, the stream leads directly to the arising of the Dhamma eye, the vision that actually constitutes this first awakening. Over time, the stream ensures that — in no more than seven lifetimes — one will be totally unbound.
This definition relates it to The Noble Eightfold Path.