Enhanced Sitelinks are almost identical to the traditional sitelinks that Google offer. They are a follow-on from the new campaign type that Google released recently. Enhanced Sitelinks allow you to replace individual sitelinks more easily as well as be able to schedule when they show independently to the campaign scheduling.
The new sitelink format allows fewer characters in the link text (now 25 down from 35), however, you can specify additional text that will occasionally be displayed along with your main link if you have existing adverts in your account that are similar to the specified text. For campaigns that are eligible to be shown on mobile devices, you can elect different sitelinks to be preferred when people search on mobiles or desktops/tablets. As always, your advert needs to be shown above the organic search results in order to be eligible to display sitelinks.
Starting from October 23rd, Google will automatically update any remaining legacy sitelinks to the new Enhanced Sitelinks without penalty as long as none of the original link text is longer than the new 25 character limit. To make sure that all sitelinks are transitioned successfully, we will manually update any existing sitelinks before October 23rd on your behalf.