I can't say I've come across this one before but I've just done some brief research and basically it appears to be a fake traffic website, as the name would suggest.
Sites like this work on a scheme where you visit sites in their list of "members" and this earns you credits. The more credits you earn this way, the more people can visit your site. Think of it like exchanging visits.
I've never used one of these myself but I'd imagine there will be certain criteria that must be met to earn the credits; maybe a certain time on page or performing an action so you're not generating a bounce.
A bit more info I found on a black hat forum:
"...easyhists4u is, alike others, website service, which will give you plenty of free and real traffic, however, to get the free traffic, if you don't wanna pay for it, you firstly need to earn credits and to earn credits, you need to browse other people's websites, then you earn credits and you can exchange those credits for a free traffic. It's simple and easy, but the catch is, you're trading your own free time for your traffic, which is kinda a deadend, because you need to spend like 1 hour to get enough credits for like 10 visitors to your page, which is kinda a joke, if you think about that."
As for the question of how this benefits you, real and engaged traffic has been proven to help your rankings in the short term. It stands to reason that continuing to pay for traffic every day would offer you continued improved rankings as a result of this traffic. I don't condone this sort of thing since it misses the true point of SEO and just focusses on SERP positions.
Finally, how your client was selected is one that I can only speculate on. I'd suggest it's either a previous SEO provider submitted them to this scheme so they could report "traffic growth" to the client. Alternatively, the owners of this site fake traffic site could randomly select domains to drop into their members list so that people do exactly what you've done here - notice them in the referral list and look closer at them.
All in all, I'd suggest contacting them and attempting to have the site removed from their list and adding them to the disavow file as well. It's unlikely you'll get a response from them but it's worth the 60 seconds it takes to send an email anyhow.
Fake traffic like this is painful because it completely messes with your stats and forces you to mess around with filters to exclude them as a referral source.