Shellcode traditionally meant binary that would do something like exec("/bin/bash") (i.e. code that launches a shell). When abusing a buffer overflow, you would usually want to somehow get this code to be executed. Later, the term expanded to mean any kind of user-provided bytes an attacker wants to be interperted and executed as machine instructions.
If you want to hack a system, the ideal program you want is a command shell. And if you exploit a program with elevated rights, then you could get a shell with elevated rights which would let you ultimately take control over the system.
Edit: And if anyone wants to learn about computers/programming, I suggest you try it yourself. It's an excellent way of learning how the system works at a low level.