# Meaning of Qqnorm plot in R

I am testing the normality of a sample with R using qqnorm. I obtain this:

I understand that the meaning of this plot is that the sample has fat tails. But what is the meaning of the values on the $x$ axis? Are they standard deviations? Are they quantiles?

If they are standard deviations, I understand that more than 99% of points follow quite nicely a normal distribution. If they are quantiles, I can only say that for 2/3 of the points. However, it looks really nice here: