Atlaskit is the technical implementation of the Atlassian Design Guidelines. It is a collection of reusable components that can be downloaded independently into your projects. Atlaskit components are built for React.
Each component is also independently versioned and published to npm. The full list of components can be found in the Atlaskit Registry. The source code can be downloaded from here, or can be cloned from the bitbucket vcs.

Atlaskit is a mono-repo, which means that different parts of the repository can have different licenses. The base level of the repository is licensed under Apache 2.0. There are separate license files (LICENSE) for each component under /packages that specify the license restrictions for each component. While most components are licensed under the Apache 2.0 license, it is worth noting that packages containing styles, assets & icons are most likely licensed under the Atlassian Design Guidelines license.