Google are stating very clearly what are Dart’s goals:
1. A new better web programming language, that could be updated and adoptive.
2. Written similarly to existing languages, so web programmers can learn it fast and easily.
3. The language will deliver high performances for all web browsers and devices (PCs, tablets, phones, etc).
Dart is an open source language and it still on its early development stages. If you want to test and learn about it, you can visit dartlang.org (by Google) where you can find tools and guides for it. Google encourage developers and programmers to take a part in its development by providing reviews and feedback on the site.
Future Implications Assumptions
I am pretty positive that it will stick and serve as the future default web language alongside HTML5. I do not expect however the transition will occur in the next 1-2 years, it will take more time and development until it will be fully ready and adopt by the web.