"To impress the employer" means to make a positive impact on the person who might hire you for a job. It involves doing things that show your skills, qualifications, and qualities to make them see you as a good fit for the job. Full definition
In many cases, internships can also result in a full - time job if the opportunity is available and you really impress the employer with your work. (reed.co.uk)
To impress an employer in today's highly competitive job market, you must stand out. (resumebymarissa.com)
Cover letters usually lead to interviews, but sometimes, they do impress employers enough to hire you without interviewing you. (coverlettersandresume.com)