Before you get too excited, the free battery replacement is for 13-inch MacBook Pros only. Apple rolled out a new battery replacement program for all the Macs without Touch Bars.
According to the page on Apple's website, a "limited number" of 13-inch MacBook Pro units shipped with a component that could fail, which would, in turn, cause the battery to expand. Although Apple ensures consumers that this is not a safety issue (your laptop is not going to explode, relax!), it is replacing batteries for free of charge.
Unfortunately, that is all we know about the issue. Apple did not provide any further details, but if you own a non-Touch Bar 13-inch MacBook Pro that was manufactured between October 2013 and October 2017, you might be in luck for a new battery.
All you have to do is head to this page, enter your MacBook's serial number. If the site tells you that your MacBook is one affected by the issue, you have a few options. You can find an Apple Authorized Service Provider near you, make an appointment at an Apple Retail Store or mail your computer to the Apple Repair Center. Regardless of which option you choose, Apple will examine your computer to make sure that it is eligible and in working condition. If so, service could take between 3 and 5 days.
Apple does, however, make it very clear that this not a way for MacBook owners to score a free repair. Additional damages which impede Apple's ability to replace the battery may have a cost associated with it, and Apple will not extend the standard warranty of your computer. The good news is still that the battery replacement program will last five years.