Peer review is the process of subjecting scholarly work to review by other experts in the field.
The term "peer review" is typically used for scientific and academic publications. When an article is submitted, it is sent to the authors' "peers" (i.e., other experts in the same field) to assess the quality of the work. A similar approach is generally taken to evaluate research proposals submitted to agencies for funding, such as the National Science Foundation (U.S.) or Natural Sciences and Engineering Research Council (Canada), where the proposals are sent out to qualified scientists to assess whether the proposed projects merit funding.
Approval by peer review is a necessary but not sufficient criterion for quality work. It mostly judges basic competence, such as minimizing the chances that pseudoscience can masquerade as science, and filters out trivial or low-quality work that would not contribute anything of value.