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"The “h-index” was introduced in 2005 as a metric for estimating “the importance, significance and broad impact of a scientist’s cumulative contributions.”
It takes into account both the number of an individual’s publications and their impact on peers, as indicated by citation counts.
Its creator, Jorge Hirsch (UC-San Diego) asserts that

a “successful scientist” will have an h-index of 20 after 20 years;
an “outstanding scientist” will have an index of 40 after 20 years;
and a “truly unique individual” will have an index
1. of 60 after 20 years
2. or 90 after 30 years.

— CARNEGIE INSTITUTE OF WASHINGTON
The h-score essentially gauges your impact on the field of science as a whole.
It answers the question: “Have you help move your field forward?”
It depends on field but,

Average is ~10,
successful is 20,
outstanding is 40,
60 is the realm of Nobel Laureates.

What is [Professor] Dr. Peterson’s score?
As of 2018 Peterson has an h-index of 51 on Google Scholar
[Website editor as of 2021 it is now 55]
Jordan B Peterson — Google Scholar
According to studies, 62 is the average of Nobel Prize winners, which is a number Dr. Peterson is slowly encroaching on.
He’s one of the top 50 most cited clinical psychologists of all time with over 11,000 citations.
[Website editor as of 2021 it is now 15698 ]
So is Dr. Peterson worthy of the title that the New York Times gave him of
“the most influential public intellectual in the Western world right now”?"
chrisvacc.medium.com/jordan-peterson-what-are-his-credentials-in-academia-393e1fb04494