The peer-reviewed scholarly record is the basis for building further knowledge. While the peer-review process is not perfect, it provides some quality assurance for the material that ultimately passes review and is published. Moreover, legitimate scholarly publications serve as an archive of this record, maintaining our ability to access and use this knowledge through time.
Predatory publishers fail to fulfill either of these obligations. They have minimal or no peer review of submitted manuscripts, and there is no guarantee that the journals they publish will persist through time, especially if the company goes out of business. Another problem is that even when they do publish good research, the work is likely to be ignored, because these journals are often not indexed in major databases and other scholars do not read them.
Worst of all, authors pay for the privilege of receiving these dubious services.
While even some legitimate publishers will fulfill one or more of these criteria, they do indicate a potential problem. Proceed cautiously with publishers that display a few of these issues, and avoid them altogether if most of the list applies.