What is the importance of <h1> tags when it comes to on page optimization?

the heading html tag "h1" modifies that that heading text is the most important in the page . when search engines try to capture any search possess , it always look for h1 heading then h2 heading down the grade until h6 .

that mean h1 is more important than h6 , so that we use it in heading 

While keyword prominence is still an important ranking factor, whether it is within the H1 or simply highlighted at the top of the page, there is another level to the effect of the H1 tag on organic search performance. A page’s ability to effectively engage users is another way Google organizes its search results. The bounce rate is arguably the most important engagement metric as measured by Google’s algorithm.

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Hello,

Simply, It highlights the most important heading title in your page, so the browser can show this Title

also when it comes to SEO, It guides the search engine to show this title on search result and link it with other SEO algorithms (Keywords in link, discretion and text) 

Thank you

The H1 tag is the most important heading because it’s the highest level tag that shows what your specific page is about. Search engines generally give this tag more weight over other headings, so it usually improves your search engine ranking when you use it correctly and in conjunction with other onsite SEO techniques.