Mathematicians like to use parametrizations to measure "how |any dimensions" something has. If you need two indexes to traverse it (x and y), it's 2d, if a single index works best to describe it, it's 1d.

Another way to think of it is "there is semantic meaning to 'the character to the right/left of this one', but is there to 'the character above/below this one'?" In most programming languages, there isn't at all.