A bad link (also "broken link") is a link to a website that does no more exist or which's content has changed in way it is no more intented to link to. As the Internet and it's contents change very quickly bad links are not unlikely to be encountered.
"Bad link" could also mean a link to a website which is suspected by a search engine of manipulation and there is considered being a "bad" website. This evaluation is made from the search engine's point of view and does not automatically mean the accused website's content is really bad - even though it very often is.
Many owners of websites fear that linking to (too many) bad sites would bring a website into suspection of manipulation and finally being ranked as "bad" as well. Whether search engines follow the concept of "bad websites" and which consequences a bad website would suffer then is not known as the algorithms of search engines and their concepts of evaluation are kept secret in general.
In general it makes sense to trust that a link towards the own website from such a bad site could do no harm. So in worst case it is useless for the own pagerank but would not decrease it. This is because no one could deny another site to set a link to one's own website. So it would be unfair to punish someone for something he could not influence.
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"They came to see and to be seen as well"
- Ovid
- Ovid