Linux is an example of an open source operating system. Linux applications can be developed using different programming languages like Python, C, C++, VB.net. All this will be determined by whatever you want to do and the kind of application you want to develop.
I would however choose Java programming language. If you want the app to be portable to windows, then IMHO, Java is the best. Learning a little C programming and doing some python scripting is recommended if you want to learn the Unix way. C and JAVA are best recommended if you want make Linux applications as a career.