Backlinks equate to a vote of confidence from other websites. It is as if you have other websites proving the legitimacy of your website.
Like the TripAdvisor review, they recommend people on your website.
If you need to link to a website you do not trust, you will label HTML as rel = nofollow. So dofollow links are a colloquial term for good, reliable links.
Technically links are non-compliant links unless they are made into non-compliant links.
Not all links are created equal. The higher the page rank in the Google page rank, the better we look at your link.
Illustration; Amazon link or sky news or mayo clinic would be great, a link to tom's shady deals to steal all your money mwa ha ha - it will be ignored, or it will negatively affect the quality of your page.
Dofollow links are the backlinks that will make your page rank higher in search results.
I give you some dofollow backlink list below: