What is Busybox?
BusyBox provides several stripped-down Unix tools in a single executable file. It runs in a variety of POSIX environments such as Linux (including Android), FreeBSD, and others, such as proprietary kernels, although many of the tools it provides are designed to work with interfaces provided by the Linux kernel. It was specifically created for embedded operating systems with very limited resources.
There are several Busybox implementations for Android, the best known probably is Stericson's BusyBox.