Dart is a recent programming language. Originally proposed by a team at Google in 2010, its main purposes were to be a flexible, but structured language for the web. Its syntax was (and still is) very close to other languages (namely Java or C#) which makes it easy for newcomers to start using Dart.
Nowadays there is a new main purpose for the language: Flutter. A project that has been unveiled in 2015 and that utilizes Dart as its programming language. Currently developers use the project to deliver native cross platform mobile apps to both iOS and Android. In the future there will be other compile targets such as the web, or desktop applications.
The Eclipse IDE was once heavily used for Android development. But with the addition of a dedicated IDE for Android development (Android Studio) Eclipse is no longer the preferred choice for Android development as the tooling did not receive updates anymore.