Most commonly it is not a very big moment. The first one is important as a major milepost, though, because for most people this will mark the beginning of an acceleration of their spiritual/meditative progress. It might be important because if you are constantly working up to a high equanimity and not getting a fruition, ever, after years, who knows, maybe it might be a signal to change something, increase the dose, work with a teacher, whatever.
I think the word cessation is probably the best English word to use for this neurological phenomenon. This is one meaning of the word nirvana, an extinguishing. Also known as a fruition, being the so-called fruit of the path.
When the mind is in high equanimity (11th nana according to the Progress of Insight) and one truly lets go and is okay with everything, there can be a little discontinuity, a "blip" where one loses time, perhaps a fraction of a second. A common response is "what was that?" It is as if the mind lets go of the "self" for a moment, or "reboots". In that moment there is nothing - no seeing, no hearing, no taste, no smell, no physical sensation, no thought, no sense of time or space. If eyes are open, it's kind of like a blink.
But it is very brief, and it seems the mind has this strong bias to assume everything is "normal", that things are continuing as before, and so you have to really be aware and see things as they are in order to notice this. But it's not like you really see it, it's more like you pick up the edges of the event horizon on either side of the black hole, you perceive the glitch, and some describe picking on some clues as to the lost time - i.e. "wait, my breath was at the bottom, now it is at the top". This blip moment is often immediately followed by a flash of light (technically, one is sent "back" to the 4th nana), often followed by a somewhat blissful wave of sensation through the body.
This phenomenon will eventually repeat, and can come in a variety of slightly different forms.
Some of these seem to be "deeper" than others. For stream entry, it apparently has to be deep enough to do the damage, as it were. It is as if something is seen through or perhaps the mind, constantly trying to understand and deal with it's surroundings, is confronted with the possibility that instead of being something, perhaps it is nothing and must take that information into it's calculations. That seems to change something. Stream entry is generally followed by a "honeymoon" period where one's mood is very good and concentration is excellent. Jhanas may become more obvious.
Some people can bring these on at will, and I have heard that Judson Brewer at Yale has recorded some of these with fMRI, but I suspect he will need a much larger sample before we begin to get a clue as to what is going on with this.
From the Heart of Wisdom Sutra:
So, in emptiness, there is no body,ADDENDUM:
no feeling, no thought,
no will, no consciousness.
There are no eyes, no ears,
no nose, no tongue,
no body, no mind.
There is no seeing, no hearing,
no smelling, no tasting,
no touching, no imagining.
There is nothing seen, nor heard,
nor smelled, nor tasted,
nor touched, nor imagined.
I guess this post was for people that are experiencing relatively straightforward cessations. I should mention that also people might notice nothing more than a shift in awareness, a relatively sudden and significant increase in their mindfulness ability. And technically, it could plausibly happen so slowly that you would never notice anything.
But yeah, if you're noticing these blip-flash-bliss wave moments repeatedly, and particularly if you are experiencing the shift in mindfulness, maybe noticing jhanas for the first time, yeah, that's stream entry.