Link Farm (verb) refers to the attempt by a website owner to artificially increase the authority and page rank of a certain webpage, by backlinking from several low quality websites built with the sole purpose of participating in link schemes.
Link Farm (noun) refers to websites with low quality content, whose only purpose is to link to other websites.
Link farming is illegitimate and heavily penalized by search engines.
Link farming is an illegitimate, black hat SEO technique employed by website owners that are trying to artificially increase their authority and page rank, by backlinking from, most often, low-quality websites that were only created for hyperlinks in the first place. This technique is meant to trick the authority page rank system search engines use, by giving the appearance that the target website is much more popular and quoted than it really is. Link farming is harshly penalized by search engines and is usually on the top of the list of things you should never do for SEO.
When webmasters used this strategy to full extent, they would automatically generate hundreds or even thousands of low quality websites themselves. They would then proceed to fill these pages with an equally high amount of hyperlinks, creating what we call a ”link farm”. These link farms would be all interlinked or, at least, all of them would point to the same webpage (the one meant to rise in the page ranks). Owners of such networks of link farms would also use them to sell bulk links to others who wanted to benefit from a large number of quotations all at once.
When link farming still worked, before some core updates from Google were applied to stop it, the results in search engines were affected in terms of relevance, with relevant websites likely pushed back by low quality content websites that benefited from an impressive amount of backlinks they had probably bought. Obviously, this was handled by Google and all other search engines that wanted to maintain the relevance of their search systems.