A para-site is a website that lives off the popularity of another (usually very popular) web site. Para-sites do this by spamming links pointing to their own site on another more popular website to gain traffic.
Because the web sites these para-sites spam on have so much traffic it means that even if they manage to siphon off only a small percentage of visitors they still get a lot more hits than they would have usually. (mainly because para-sites alone are of little interest to the average Internet user and of low quality)
Most para-sites will also have a lot of advertising on their websites. This is so they can gain revenue and the main reason para-sites exists. To make money without any effort and by the popularity of others.
The name originates from the real term "parasite" which means:
"A plant or animal that for all or part of its life obtains food and physical protection from a living organism of another species which is usually damaged by and never benefits from its presence. A person who lives at the expense of others, contributing nothing in return."
Para-sites would not exists without the large and popular sites they "feed" off.
For example on the known video site 'youtube.com' which allows comments, para-site owners or their bots will try and spam comments containing links to their own site, that lead to their site to gain more visitors and hits.
Another very good example is on the site "RottenTomatoes" where para-site owners and bots will spam what seem to be vaguely helpful links to images and "previews" of movies in the comment section of a movie release review, in order to try and get you to go to their site and make them money.