Important relationship between current and voltage in a bipolar diode.
Due to the expressive slope of this curve after ~0.65V, a little change in Vd reflects a large one in Id. So, in usual applications, when the diode is forward polarized, there is a large range of current where the voltage can be approximated by a value next to ~0,7V.
Note that in this simulation the current is approximately Id = (V - 0,7)/R, when conducting.