An applicant is someone who signs up or applies for something. A job applicant for example, often fills out a form and then interviews for the position she hopes to get.
When you submit your college application to a school you'd like to attend, you are an applicant to that school. Other kinds of applicants are job candidates and scholarship hopefuls. To apply is to put in for or request entry to something, and the root of both apply and applicant is the Old French aploiier, "apply, use, or attach," from the Latin applicare, "attach to, join, or connect."