I know $\mathbb{R}$ is the real number line. What really is $\mathbb{R}^n$? I know $\mathbb{R}$  is the real number line. What really is $\mathbb{R}^n$?

EDIT (based on comments below): What actually is the result of a cartesian product? That is something I failed to grasp too. What do you get when you multiply the number line $\Bbb{R}$ with itself? I mean the final result? Thanks.

It is Euclidean space, which can be thought of as ordered $n$-tuples of real numbers.  
For example, $\mathbb{R}^3$ is the set of all ordered triples $(a,b,c)$, where $a,b,c\in\mathbb{R}$.  
