hx-boost is an attribute from htmx, a small JavaScript library that lets ordinary HTML send its own HTTP requests. Put it on a parent element and htmx upgrades the links and forms inside it, so they load in the background instead of reloading the whole page.
For example:
<div hx-boost="true">
<a href="/about">About</a>
<form action="/search" method="get">...</form>
</div>
Clicking the link fetches /about with AJAX, replaces the page body with the response, and updates the address bar and browser history, so Back and Forward still work. Without JavaScript, the links and forms behave as normal, which is the point: the page still works if the script fails to load.
Two things to know. The whole body is swapped by default, so any scripts or state outside the new content can be lost. And the server should return a full page, as it would for a normal visit, so boosted and unboosted requests get the same result. You can turn it off for a single link with hx-boost="false".