A blind audition is a term used both for theatrical and musical auditions.
In the context of a theatrical audition, a blind audition is an audition for an actor where there is no script for them to read from and they have to improvise lines. As an example, Eva Green's first audition for the James Bond film Casino Royale was a blind audition.
In musical auditions, a blind audition is one in which the person auditioning performs from behind a non-transparent wall or screen. This assures that those deciding on the musicians make their decisions only on the performance and not the appearance of the performer. Art Davis is known for launching a legal case which led to the current system of blind auditions for orchestras [1][2][3]