You're seeing them in Analytics?

If so...
[searchenginejournal.com...]

It is referrer spam. As pointed out by RhinoFish.

Are these signs that the website that appeared in the traffic program has bought a service that gets more traffic to your website?

No, quite the opposite, it is fake traffic. The requests were made directly to the Google Analytics end point, with fake referer data. If you look for this traffic in your raw server logs it will not appear as there were never any requests made to your server.

The goal of referrer spam is to get Webmasters that watch their traffic, to think "Oh look a new referral, thus a new link! Let me see where it is coming from." Then the unsuspecting webmaster follows the referrer path to a website, a site that can potentially contain malicious code or to simply promote some spammy service.

This spam can be easily filter in GA, but not as is recommended in the article linked by RhinoFish. That method works but only specifically for referrers that you have already seen.
The most effective method is by setting a filter that only allows traffic from the hostname == your domain.

Thanks much @NickMNS and @RhinoFish. I'll check into it.

One place to start (just mentioned earlier today in a different thread) is here: [webmasterworld.com...] though that case was in relation to GA and invalid traffic. A search here for referer spam turns up a lot of reading.

This is an on-going problem! Learning how to deal with it is essential to keep logs "readable" for real traffic. :)