A person who is competitive,overly-ambitious and substantially exceeds minimum requirements. A gunner will compromise his/her peer relationships and/or reputation among peers in order to obtain recognition and praise from his/her superiors.
That chic in the front row of our class who always raises her hand, takes on additional assignments, and wrote a 25 page answer on our final when all that was required was 10 pages is such a gunner.
A person (usually a medical or law school student) who uses over 3 different colored highlighters, tabs every page in their notebook, and raises their hand after every question asked by their professor, regardless of if they know the correct answer or not. Gunners like to hear themselves speak. They use complicated words to make themselves sound smart even though they have no idea what's going on in class- they pretend they do. They are trying to intimidate you and eliminate competiton.
This gunner in my Chemistry class answers every question the professor asks, asked 5 questions during a 1hr class, and uses 8 different colored highlighters.