The Arduino microcontroller is part of a large community of makers and is powerful enough to cover a wide range of applications. The BeagleBone Black is also a popular prototyping platform, but is from another world than Arduino. The Black is a single board computer powerful enough to run a full version of Linux.
If you have a BeagleBone Black and an Arduino, you can unify the platforms and build new prototyping systems able to perform a wide range of operations.
If you have a BeagleBone Black running the Debian Linux, an HDMI cable, a power source, and an Arduino microcontroller, you can check this tutorial and start to setup the Arduino IDE from the BeagleBone Black board.