When a phone is rooted, one of the most common things to do after rooting is the installation of the BusyBox binary, prior to running any applications that require root privileges.
To make sense of this, it is necessary to have a brief understanding of what BusyBox is. BusyBox is a collection of powerful command-line tools in a single binary executable that can be run for UNIX based systems, including Android. The collection of tools available depends on how the BusyBox binary was built, and the source code is GPLv2 open-source, available from http://www.busybox.net/. Many of the tools don’t do anything useful without elevated root privileges as in a rooted Android device.
Many Android applications that require root privileges use BusyBox from the command-line extensively. Some of the utilities are powerful enough to severely alter your device, such as the ability to write data directly any partition on your device. Many third-party firmware packages including Cyanogenmod utilize BusyBox extensively and already come with prebuilt with it, so users should be aware of consequences if making any modifications to the existing installation of BusyBox, by themselves of from one of many pre-packaged Play Store applications.
Keeping it on your device usually isn’t going to be a problem, but keep in mind that this tool can be destructive for your device and can make your device open to vulnerabilities compared to a stock shipping device. If you use the command-line a lot, you probably know what it is already and want to keep it installed.