According to Dictionary.com, native when referring to computers means:
“designed for use with a specific type of computer”
And when you’re talking about applications on mobile devices, that’s what it means. A native application is one that has been written for iOS (iPhone and/or iPad) or Android, and is not HTML repurposed. Most web applications are not native to any mobile device, and as such can run on any of them as well as desktops and non-smartphones.
Plus, the most common reason people want to make native applications rather than web applications is that you can sell them in the various app stores. While it is possible to sell web applications, it’s much more difficult and most developers end up offering their web applications for free.
So if you decided to forget about HTML5 because you couldn’t use it to create native iOS or Android applications, you should think again and consider using a program like PhoneGap (or SenchaTouch or one of the other tools out there) to convert your web app to a native app.