In case of prefetching, that's a header <link> functionality: https://developer.mozilla.org/en-US/docs/Web/HTTP/Link_prefe.... Most implementations use it for static content like images or CSS. There's also DNS prefetching, which depends more on the browser.
What you might mean is "prerendering", i.e. silently downloading another page in the background. This feature is not yet supported in Firefox, but heavily used by Google and in Chrome. IIRC, earlier Firefox versions actually supported this through addons, but these addons did not know the page and pre-loaded every link they could find on the page. This resulted in an enormous amount of background traffic, essentially wasted due to only one link being the "next" link. Therefore, using the preload/prefetch/prerender link attributes should be left to the site owner.
What you might mean is "prerendering", i.e. silently downloading another page in the background. This feature is not yet supported in Firefox, but heavily used by Google and in Chrome. IIRC, earlier Firefox versions actually supported this through addons, but these addons did not know the page and pre-loaded every link they could find on the page. This resulted in an enormous amount of background traffic, essentially wasted due to only one link being the "next" link. Therefore, using the preload/prefetch/prerender link attributes should be left to the site owner.
Here's a good resource on preload (same page), prefetch (next page) and preconnect (other source domains): https://www.machmetrics.com/speed-blog/guide-to-browser-hint...
Edit: as Arkanosis mentioned in a related comment, the refered to addon was called Fasterfox: http://fasterfox.mozdev.org/faq.html#What_is_prefetching