If person is a qualifier, they've done well enough at some sport or activity to make it into an important competition. Qualifiers have made it into the big league.
When a word, rather than a person or a team, is described as a qualifier, it means that it modifies another word. Grammatical qualifiers are often adjectives. In the sentence "That is a fluffy cat," the word fluffy is a qualifier, attributing a specific quality to the word cat. The root of qualifier is the Latin qualis, "Of what sort?"