Amazon Echo owners can ask Alexa for free audiobooks if they're a first-time user of Audible, Amazon's audiobook service where you normally have to pay for each book you want to listen to. There's no catch it seems either. Amazon is just hoping that people who try an audiobook and listen to it and enjoy it to the point that they'll decide they want to listen to more audiobooks and then sign up for the Audible service, though it's worth keeping in mind that to use Audible continually beyond the free trial period you will need to pay $14.99 a month.
If you own an Echo, Echo Dot, Echo Show, or Echo Plus, you can ask Alexa to read any Audible audiobook whether it's an old classic or something new that was just released as it seems there's no limitations on the books you can choose. This is a good thing for anyone who might have been interested in trying Audible but only if they had the opportunity to try it with a book they've been wanting to read. It's perhaps a perfect way for Amazon to entice consumers to choose it over Play Books when it comes to the audiobooks, as Google's service doesn't come with a monthly fee which has made it the go-to choice for some.
That said, Google's Play Books audiobooks were given out for free as well during the initial launch of audiobooks on the Play Store for customers that owned a Google Home device, allowing them to pick an audiobook and keep it which could then be played through the Google Home or any device with Google Assistant. There were no limitations here either really, so this might be Amazon's way of competing with that particular freebie offer that Google started a couple months back. It's unclear if Amazon is placing a time limit on this but it doesn't appear there is one, so if you don't own an echo yet you can still buy one and then once you receive it ask Alexa to read you an Audible book of your choosing. The same goes for people that already own an Echo but just haven't had time to choose a book, so waiting a week likely isn't going to lock anyone out of this offer.