Thorup : What is the meaning of super distance?
It says: "For each vertex we have a super distance $D(v)\geq d(v)$"


"Super" refers to the "$\ge$" relation between $D$ and $d$. In other words, since $D(v)\ge d(v)$ where $d(v)$ is the distance from $v$ to $s$, $D(v)$ is called super distance.




  Is it just a distance value from origin while calculation until $D(v)=d(v)$ ?


Correct. It is just a distance that approximates the shortest distance from the source from above, which will become that shortest distance at the time $v$ is moved to $S$, the set of vertices whose distances have been settled.