"To fit the profile" means that someone or something matches the characteristics or description of a particular type of person or thing. Full definition
There's no point in pursuing someone that doesn't fit the profile of a person you'd be interested in dating. (digitalromanceinc.com)
Often you will find that you may not fit the profile of a perfect applicant, but this doesn't mean a program administrator would not value your presence. (sciencemag.org)