And these quizzes are shown when you are just about to forget the answer so that you can knowremember the answer of the quiz until you die (AKA Spaced repetition).

The intro part of my blog post about "Incremental Reading".

Could also say "introduction"

No need to say part, it is redundant. the intro or introduction is a part of your blog post and we can already assume that information.

Incremental reading (IR) is a way to read articles on the Internet very efficiently. ¶
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"very" disrupts the flow of the sentence here. As a general rule of them, it always sounds better to use either a strong word or just not have very in the phrase.

very tired = exhausted
very happy = elated

I am very smart = I am intelligent.

Very is grammatically correct but I advice against using it.

InUsing incremental reading, you'll extract the important pieces of the article, simplify the piecesm, and create quizzes by creating a cloze test.

Tense - also I changed it to using to better articulate the demonstration (using this process)

added "the" to important pieces to emphasize that you are only extracting pieces that are important and not just any piece.

Changed simplify the pieces to simplify "them" - we know you are talking about the pieces so do not need to restate that. It flows better changing it out into a pronoun. You can hear this in this example: "Julie walked over to the flowers and then Julie picked a flower." It sounds unnatural and is hard to say. By switching out the already known situation for pronouns, it sounds and flows better: "Julie walked over to the flowers and then she picked one of them." You could even omit "of them" in this example because it is obviously that "picked one" would be referring to the flower.

And tThese quizzes are shown when you are just about to forget the answer so that you can know the answer of the quiz until you die (AKA Spaced repetition).

Technically, shouldn't write "and" at the beginning of a sentence when writing, but we say it out loud all the time. As this piece feels like a formal, informative piece, I omitted the and.

The rest of it is grammatically correct so I'm leaving it, but I suggest saying something more like:

The quizzes use the "spaced repetition system", which is when the questions are asked right before you are about to forget it in order to store it into your long-term memory.

This is just a more accurate example of what SRS does and how memory works; it is a hyperbole to state you will know the answer until you die if you used SRS.

The intro part of my blog post is about "Incremental Reading".

I think 'part' is fine, but a little inelegant.

In incremental reading, you extract important pieces of the article, simplify the pieces, and create quizzes by creating a cloze tests.

As a general writing tip, I would explain would cloze tests are.

And tThese quizzes are shown when you are just about to forget the answer so that you can knowremember the answer of the quiz until you die (AKA Spaced repetition).

The intro part of my blog post about "Iincremental Rreading".

"Incremental reading" doesn't need to be capitalized or in quotations because it isn't a title.

In incremental reading, you extract important pieces of the article, simplify the piecesm, and create quizzes by creating a cloze test.

What you wrote is fine too, but since you already mentioned "pieces", it can be replaced with a pronoun instead of repeated.

AndThen, these quizzes are shown when you are just about to forget the answer, in a spaced repetition format, so that you can knowremember the answer of the quiz until you die (AKA Spaced repetition).