Backlinks cleaning is a process which appeared with the fears associated with Google Penguin launch which aimed at penalysing websites with too many inorganic backlinks.
Backlink cleaning is a complex process. The first step is to track backlinks and to identify bad or inorganic links. It can be made with devoted SEO tools or Google Webmaster Tools which may sometimes send inorganic backlinks alert.
The second and most difficult task is to obtain bad links removing. Webmaster have usually no time for the operation. In a paradoxal situation, we may meet webmasters asking for removing backlinks they have asked or paid for.
Because it is often difficult to obtain suppression of inorganic links and because some of them might have been created by malicious competitors, Google has launched in October 2012 a tool for disavowing toxic links in GWT ( see Google link disavowal tool).
Backlink cleaning has probably been a little over-publicized by SEO vendors and new softwares or functions in SEO tools have been developped.
A panicked webmaster:
A bad links cleaning software: