If you self-publish your work, you have the option to sign up for Amazon KDP. There are pros and cons to the program, but basically, you agree to give Amazon exlusive rights to sell your book for a set period of time in exchange for a few added features. For example, in KDP you can be part of free Prime lending. Readers can basically rent your book for the month for fee, then you get a cut of the Prime fees that month based on the number of readers who selected your book for their free lending book that month. Another opportunity is to list your book for free.
Free can be a powerful selling tool. If you are an unknown author, readers may be hesitant to purchase your books without knowing if they will enjoy your style of writing. A free promotion period allows them to try you, risk free. Ideally, they will become a fan and next time you have a book release they'll be willing to pay.
The downside of free days is that so many authors are utilizing their free days at any given time. In order to maximize your exposure, you need to get the word out. This is a great time to send an email out to your mailing list. Ask them to pass along the word and maybe even offer to do a prize drawing for your mailing list if you hit a certain number of downloads.
If you aren't self-published, you won't be able to sign up for KDP and it's unlikely your publisher will be interested in a free promotion. However, it never hurts to ask if they'd be willing to run a sale on your book for a set period of time in order to attract new readers. They will probably be more receptive to the idea if you, or your agent, reach out to them with a preset promotion plan in place for how you plan to make the best use of the sale.
No matter how you do it, keep in mind that there are literally thousands of free or deeply discounted ebooks available on Amazon every day of the week. If you want yours to stand out, you'll need to do more than just slash the price.