Oh my, another handwaving article about Big O Notation. Why does everyone and their mother feel the need to explain this thing in "plain English".

"Big O notation seeks to describe the relative complexity of an algorithm [...]" Relative to what? To the moon and the stars? Big O is a notation to describe the growth rate of functions.

Therefore, you can also use it to describe the memory usage of an algorithm. Even if the author of the article thinks otherwise.

And so on and so forth.

Seriously, I understand the wish to explain this thing clear and simple. But what is so hard about a clear and concise description using maths and some plots?

Or, in John McCarthy's words:"He who refuses to do arithmetic is doomed to talk nonsense.".