Profile backlinks are those backlinks in which you can create profile on business profile website, there you can create hyperlinks of your website.
Some considered it as black hat, some call it grey and some call it completely white hat. Profile link building is one of the lowest quality back links but easy to create which give more room to create huge number in short period of time. This also shows some positive results in ranking if your back links from profile page are keyword anchored and dofollow.
Profile backlinks are simply links you put in forum profiles, like your profile right here on DP. Forum software openly gives you a place to add your link, so you're not doing anything bad in that respect. However, of you are creating forum profiles exclusively for the purposes of getting links, that's generally considered spam. Certainly it works, but like everything, you should use it in moderation and as part of your overall backlink mix. Google likes to see links coming from all over. If you only had profile links, that would look unnatural.