Ruby is what's known as an interpreted programming language. It was invented in Japan by a guy nicknamed Matz. You write code, save it to a file, and then a separate program "interprets" this file into code that the computer can understand.
So, when people refer to "Ruby," they are most commonly referring to two things: the language, and the default interpreter. The default interpreter is known as "MRI," which stands for "Matz's Ruby Interpreter."
Rubinius is an alternative Ruby interpreter. It's main claim over MRI is that Rubinius has (much) better support for multi-threaded applications. Additionally, where much of the core Ruby functionality (e.g., Array) is built using C in MRI, Rubinius builds most of it's core functionality using pure Ruby code, and relies on the interpreter to make it fast enough, similar to PyPy. The theory is that if you build a fast enough interpreter, it's easier to build your dynamic language functionality in the dynamic language, rather than in C.
So, when people refer to "Ruby," they are most commonly referring to two things: the language, and the default interpreter. The default interpreter is known as "MRI," which stands for "Matz's Ruby Interpreter."
Rubinius is an alternative Ruby interpreter. It's main claim over MRI is that Rubinius has (much) better support for multi-threaded applications. Additionally, where much of the core Ruby functionality (e.g., Array) is built using C in MRI, Rubinius builds most of it's core functionality using pure Ruby code, and relies on the interpreter to make it fast enough, similar to PyPy. The theory is that if you build a fast enough interpreter, it's easier to build your dynamic language functionality in the dynamic language, rather than in C.