A thorough and diligent review of a prospective person or project prior to a hiring or investment decision. Vetting most often refers to an individual or group, such as how a board of directors will "vet out" a prospective CEO or other top management position. Vetting of potential suppliers of a contract or business service is a common practice for the managers of a publicly-traded company, where past business results, costs and personal relationships all figure into the final decision.
Today's economies are so global that vetting takes on an increasingly important role. Potential employees or business partners may be located on the opposite side of the globe, with teleconferencing and email replacing face-to-face contact and meetings. Vetting must often be done via the internet or by outsourcing parts of the process.
For investors, vetting often takes the more common name of "due diligence", the rigorous process of researching a potential investment prior to purchase or sale.