The phrase "to win this giveaway" means being chosen as the lucky person who receives or gets a prize or gift that is being given away. Full definition
Congratulations on winning the giveaway girl and what a lovely prize too! (averysweetblog.com)
I'd like to win your giveaway because of all the YA books I read, historical romance doesn't show up much in my already - read list. (victoriastrauss.com)