Xjyuk

In Do We Really Need the S-word? in 'American Scientist', the author Megan D. Higgs writes

Did the people who introduced the word’s use in statistics intend for it to be interpreted according to its current everyday meaning? The answer is not simple. In his 2001 book The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century, David Salsburg contends the word carried much less weight in the late 19th century, when it meant only that the result showed, or signified, something. Then, in the 20th century, significance began to gather the connotation it carries today, of not only signifying something but signifying something of importance. The coinciding of this change in meaning with a steady increase in its use by more scientists with less statistical training has had a big impact on the interpretation of scientific results. My sentiments echo Salsburg’s: “Unfortunately,” he writes, “those who use statistical analysis often treat a significant test statistic as implying something much closer to the modern meaning of the word.”

I did some searching on Google, but unfortunately, most results are about the term "Historical significance", and I failed to find a definitive reference about the change in the meaning of "significant".

Can you tell me about more about the meaning change, like when and why did it happen?

Salsburg appears to be wrong.

The OED gives meaning 2: "That has or conveys a particular meaning; that signifies or indicates something." from 1573; and meaning 4a: " Sufficiently great or important to be worthy of attention; noteworthy; consequential, influential." from 1642.

He might of course be right that meaning 4a was less common until the 20th century: the OED does not tell us that. But it is not true that it didn't exist until then.

The semantic shift seems very natural and unsurprising to me.

The OED dates the statistical sense from 1885.

This link explains why influential statisticians are concerned about the use of the term statistical significance.
Editorial from Nature

Their concerns are not merely linguistic, but if we just focus on those, we see that the fundamental problem is that 'significance' in statistics is a technical term that emphatically does not have the same meaning as in non-technical language.

In statistics we say a result is significant if we believe that it is not just a quirk or aberration but reflects a meaningful association (paraphrased from Whelan, naked Statistics (2013)). But a result can be significant in that sense without being significant in any other way whatever, and certainly without being " Sufficiently great or important to be worthy of attention; noteworthy; consequential, influential." In practice very few experimental results realistically can be so described, however compelling the statistical evidence for them.

The ambiguity in the word 'significant' can lead to misunderstanding about the importance of any particular scientific announcement, and ambiguity in language always offers scope for the unscrupulous to deceive people. It is improbable that the statisticians who introduced the technical meaning of significance into their subject wished for anyone to be deceived.