When a person gives her "express written consent" she directly, unambiguously and voluntarily agrees in written or electronic form to a specific term or proposition. Express written consent grants explicit permission in documented form, whether electronic or on paper.
According to the U.S. Federal Communications Commission, express written consent, as defined in the Telephone Consumer Protection Act, is permission given by someone on paper or electronically. The FCC extends the definition to include express written consent that is given on website forms, in a recorded verbal agreement or by selecting a specific telephone key when prompted.
The phrase can be understood by examining its antonym terms. Written consent is not merely an oral agreement. Express consent is not implied or assumed, according to Bouvier's Law Dictionary.