Parasite hosting is when someone places a webpage on a domain that is not theirs and intends to rank it organically.
You might want to do this if you want to ensure that anyone searching for your brand, for example, reaches a page that you own or created. For example, you might want to rank a Yelp page, Facebook page or others to control your brand results.
Conversely, others may want to rank for keyword terms by creating a page on a website with a high authority (let's say domain authority), as the page they create will inherit some of the trust and strength of the root domain. Some people rank those pages in a white hat way, others may choose to aggressively link to those pages - as they don't have to worry about their own site being penalised for it. You can see there where it becomes a gray area for SEO.
The most extreme example would be people in very spammy health niches, eg viagra, compromising a site and creating a new page to sell their products or promote their shop for a quick rankings boost. This is just outright black hat SEO and illegal, as it involves hacking into a site to create a page.
So you can see there are different degrees of parasite hosting, each with different levels of ethics. Hope this helps.