A groovebox is a self contained unit for the complete production of music. In hardware, an example of a groovebox is a Roland MC303 or Akai MPC2000, etc. For apps there are the Native Instruments imachine and Akai iMPC, both software versions of hardware units.
This is a list for all the Groovebox apps currently available for the iPad and iPhone and other iOS devices. See individual description for app if your device is supported.