An admirer is a fan, supporter, or lover. If you're an admirer of Jane Austen, you are enthusiastic about her novels and appreciate her writing.
The president of a pop star's fan club can describe himself as the star's admirer, and a college student who is crazy about her psychology professor is also an admirer. If there's someone in your life who leaves unsigned love notes in your mailbox, you can call that person your "secret admirer." In the 1700s, the word was primarily romantic, and it comes from a Latin root, admirari, "to wonder at."