The mining turtle is a robot used to mine straight tunnels the distance you specify, or dig outwards in a circle to hollow out an area. However, this is not even scratching the surface of it's huge potential.
When you right click the turtle itself, you will get a GUI, much like "Win32 Console". Our Turtley friend runs on a programming language called "Turtle-OS". You can type in "help" to get some turtle-OS help. It should give you some options for what you want to do with the mining turtle; for example, get a list of possible programs to run. Insert coal into the inventory screen on the lower right corner, and type in the program you want to run.
When you type "edit" in the GUI followed by a program name of your choice you get taken into another menu where you can write a list of commands for the turtle to follow. Once you have saved the program you have written you can go back into the first menu and type the title of your program. This lets you excavate large areas without a Quarry.
When utilised correctly, the mining turtle is a very useful and indispensable mining buddy.