This December 2019 article in Nature describes predatory publishing as:
“...entities that prioritize self-interest at the expense of scholarship and are characterized by false or misleading information, deviation from best editorial and publication practices, a lack of transparency, and/or the use of aggressive and indiscriminate solicitation practices.”
Many of these predatory publishers try to mimic legitimate open access journals on their face, yet lack the standard academic safeguards and practices to ensure only high quality research is published. Their main goal is profit. They will typically deceive authors about their peer review practices, editorial services and even editorial board to try to appear legitimate.
Predatory journals will typically publish anything for a fee. They are exploiting academics' need to publish for their own ends and profit.
Predatory journals exploit the open access publishing model of charging Article Processing Charges (APCs) for publication. This doesn't mean that all journals that charge a fee are predatory, though.
The "publish or perish" attitude in academia has made researchers a prime target for predatory publishers. Publication is usually a main driver for those looking for tenure or promotion within their institution. Publishing in a predatory journal won't necessarily help your prospects though.
The site Think, Check, Submit can walk you through the process of evaluating a journal through a series of checklists.
Things to look out for:
Please note that the inclusion of a journal or publisher in any of the "safe" lists don't guarantee that the journal is not predatory. The criteria for a journal to make any given list varies by the list creator.