Easy answer: to make new friends and fans.
Which (hopefully) brings about more friends and fans.
To be followed by yet more. And more after that. Rinse. Repeat.
Giveaways are goodwill and good business. I tried one this past weekend. I offered Dark Doses for free on Amazon for 24 hours over New Year's Day.
I figured some folks would use the day to try out the nifty new Kindle they got for Christmas. Others would be taking it easy and browsing the Kindle store in a semi sleep-deprived state. Still others love jumping on freebies because it's a no-risk way to discover new escapes and diversions (not counting any time invested for the download and actual read through). Perhaps the severely hung over folks would be punching the download button in sync with the throb within their skull.
The result for my book: over 250 downloads spread across 4 countries. Not stupendous and colossal, but I like that outcome very much. Because I'm hoping 1% to 2% of those downloads turn into reviews and ratings.
Because reviews and ratings are what leads to new friends and fans. Which then provide more reviews and ratings. Which leads to more...
You get the idea.