Codename One allows Java developers to write their app once and have it work on all mobile devices (iOS, Android etc.). It features a simulator, designer (visual theme/builder) and ports to multiple OS's.
Codename One is a mature open source project and its roots go back to Sun Microsystems (2006) where one of its core underlying components was developed and open sourced.
Codename One is open source. This includes the libraries, native OS ports, resource editor & native VM code. It also includes themes and separate related projects containing demos, skins etc.
You can understand more about how Codename One works and how the API fits into everything in this stackoverflow answer.