We can negate a verb using either 不 or 没, but they mean different things. The text is explaining the case of 不, such as in:
我不吃肉。 (I don't eat meat.)
他不做作业。 (He doesn't do homework.)
老师不想知道。 (The teacher doesn't want to know.)
我不喜欢跳舞。 (I don't like dancing.)
They're explaining that this is a "habitual" situation; this is not just at the stated time period, but persists over a period of time including the stated time period. (As opposed to: 我没吃肉。 (I haven't eat meat.) and 他没做作业。 (He hasn't done [his] homework.))
The relevant text gives:
去年我们总是吃中国饭。
We always ate Chinese meals last year.
去年我们每天都不吃中国饭。
We didn’t eat a Chinese meal during a single day.
Elementary Chinese Grammar 基础汉语语法, 2011. (pdf, p.45)
I'm not sure why they wrote it like this; maybe they just wanted to mix it up, or maybe it's an editing error and the first sentence should be 去年我们每天都吃中国饭. There are two complications here:
- the logical negation of "we always ate Chinese meals last year" is "we did not always eat Chinese meals last year" (not "we never ate Chinese meals last year", which seems to be what they want to express---habitually not eating Chinese food);
- since it's referring to "last year", the verb would typically be negated with 没 (not 不), which would not be a habitual action.
I feel like it's more normal to use 没:
去年我们没吃中国饭。
We didn't eat Chinese meals last year.
or to add a 不 before the 总是:
去年我们不总是吃中国饭。
We didn't always eat Chinese meals last year.
But the text is trying to explain adding 不 before a verb, which is not achieved in this way.
If we simply add a 不 before the verb 吃, we get:
去年我们总是不吃中国饭。
We never ate Chinese meals last year.
It sounds weird, and it's not clear to me this is grammatically correct (while there are plenty of grammatical "总是不 + verb" sentences, "always didn't eat" is a bit of a contradiction).
In short, the first example sentence isn't naturally negated by adding 不 before the verb, so they chose another sentence where 不 is before the verb.