The O stands for "Ordnung", the German word for order. So it does literally mean that, except mathematicians think that the order of f(x)=1 is the same as the o

The O stands for "Ordnung", the German word for order. So it does literally mean that, except mathematicians think that the order of f(x)=1 is the same as the order of f(x)=10^6, because "clearly" f(x)=x gets way bigger than any constant function.