Paid links are paid for links that can manipulate PageRank or be used for advertising.
On the one hand, paid links are advertisements for your business that are highly targeted to a specific audience.
On the other hand, paid links are considered a black hat SEO technique, especially by Google.
If a paid link manipulates PageRank, it is viewed as a form of link farming and your website will be penalised.
The following information is paraphrased from Google's Webmaster Tools Help page:
Google, like most search engines, use links to determine a website's relevance and authority. A website's ranking on Google search results is based on many factors, including the quality of websites that link to it. Link based rating has greatly improved Google's ability to return relevant results in a search.
However, some Search Engine Optimisers and webmasters engage in buying and selling links that pass PageRank. Doing this is in violation of Google's Webmaster Guidelines. While not all paid links violate these guidelines, links that are bought and sold for advertising purposes should be marked with a rel=“nofollow” tag.
The nofollow tag indicates that the link should not influence the ranking in the search engine's index. Google acknowledges that buying and selling links is part of the internet economy and accepts that this is done for advertising. Google has sophisticated algorithms that can detect link farming websites.
Link farming is the process where a large website buys low quality and spam-filled links and then sells them to other webmasters to use on their websites. This is frowned on by large search engines and will be severely punished. A good example of this is the penalisation of leading American department store JC Penny by Google.
JC Penny had been found guilty of using over 2 000 paid links to increase PageRank. In order to penalise them, Google moved them down to the 5th page of search results. This is just one example of how a website can be penalised by search engines.