Since the person who posed the question categorized the question under "Movies," it is reasonable to assume that he/she is speaking of the movie "John Q." Q stands for Quincy as in John Quincy...
Q in Q-Tip.
Here are two opinions:
Quilted-Tip
Quality, actually. :)
And an extra note:
Take a careful look at the capital letter 'Q'. Doesn't it slightly resemble placing a small swab...