Employment Authorization Document (EAD) is a document required by persons who want to work while they are waiting for approval of their permanent residency or based on their derivative visa status. US employers must check to make sure all employees, regardless of citizenship or national origin are allowed to work in the US. EAD is the proof that an applicant will show to their employer that they are allowed to work in the US.
An example of this would be a person that came to the US on a K1 fiancee visa, got married and filed an application to adjust their status to permanent resident would be eligible to apply for an Employment Authorization Document. Other examples of persons that would be eligible to apply for an EAD would be the spouse of a L1 transfer visa or E2 investor.