“Anchor tags” are simply the glue that makes the web work. Any link that appears on a page is, in its HTML,
<a href="the address">the text</a>
I’ll let others comment on where the “anchor” term came from (or see reference below). I think most of us simply call them “links”.
In my experience, the word “anchor” is used most often in the context of “named anchor.” Perhaps that’s what you’re asking?
“Named anchors” (aka bookmarks) can be used when you want to link directly to several places on a long page.
If the HTML on a page looks like
</h1><a name=somename></a>Major Heading</h1>
Then elsewhere on the page you can have a link (anchor) like
<a href="#somename">some link text</a>
and clicking the link will move the page so that “Major Heading” is at the top (as long as there’s a screenful of info below it on the page).
You can also link directly to that Major Heading section from *another* page with
<a href="the-page-address#somename">some link text</a>
See also:
https://www.w3.org/TR/html401/struct/links.html