This introduction does not do Logo justice but it's a start. Logo is a programming language, pure and simple. There are two models that languages come in, compiled and interpreted.
What is a compiled language?
In a compiled language the program is written and fed to a compiler. A compiler reads all your code and converts it to an executable form that your computer understands.
What is an interpreted language?
An interpreted language does not get compiled; instead, the interpreter runs each line of code as it reads it. This is a slow process, but it has the advantage of not requiring a complete compile for each change. It's ideal in a learning environment.
So have guessed what type of language Logo is yet?
Right, it's an interpreted language; at least FMSLogo is, anyway.
Logo also has another unique feature not offered in many other languages (none that I know of). That is, what's called "Turtle Graphics".
What is turtle graphics?
Turtle graphics is a simple and powerful set of commands used to manipulate a screen object called a turtle.
Why do they call it a "turtle"?
The first version of Logo used an electronic robot that resembled a turtle. The robot drew lines on a big piece of paper that was laid on the floor. In the case of a video screen (like this Logo) it's simply a cursor (or pointer) of where the turtle is.
What does the turtle do?
It draws, lines mostly, on the screen.
Turtle graphics fills a gap that most traditional languages do not. That is, it gives immediate feedback. Immediate feedback makes it fun and easier to learn programming. The purpose of Logo is to teach people (children and adults) how to program. It is modeled after a popular and powerful language called LISP and is as powerful as any other programming language.