Form I-765, Application for Employment Authorization, must be filed by certain categories of aliens to request a work permit, or in other words an Employment Authorization Document. Such categories of foreign nationals, who are temporarily living in the USA and who are eligible to work in the USA include but are not limited to: asylee/refugee and their spouses and children; foreign students; nationality categories; eligible dependents of employees of diplomatic missions, international organizations, or NATO; employment-based nonimmigrants; family-based nonimmigrants; adjustment-of-status categories.
Green card holders have right to work without requesting any special permission. If you are a conditional resident or a lawful permanent resident, you do not have to submit Form I-765.
Principal U nonimmigrant petitioners are also employment authorized incident to status. Employment Authorization Document (EAD) is issued to them automatically, without filing Form I-765 (after the underlying U nonimmigrant status petition is approved).
Employment Authorization Document proves the right for legal work in the United States. Also, EAD serves as a government-issued photo identification.
Meanwhile, Form I-765 is used not only to request an initial Employment Authorization Document, but also to replace or renew it.