There are several cutting methods one can use to cut vegetables. When you julienne a vegetable, you cut it into thin strips.
To julienne a carrot, first split it in half, so it can lay flat on the cutting board. Next, cut the carrot into about 3-4 inch pieces. Slice the carrot length-wise, then stack the slices, and make parallel cuts of the same thickness through the stack.
This method produces thin, long pieces, perfect for stir-fries and salads among other things.