What actually happens to a varicocele after it is treated with embolization?

Disappears. The embolized gonadal vein occludes and is converted to a cord of scar. Collateral veins with functional valves open to drain the area, normalizing venous pressures and allowing the dilated overpressured veins to return to normal.
Involution. The size of the varicocele (enlargement of the veins) will decrease. Embolization can be used if surgical approaches are contra-indicated as success rates with surgery are higher.
Collapse... After embolizing spermatic vein at its proximal end near renal vein, if successful, the pressure inside the dilated spermatic veins will dissipated and the affected veins will collapse and hopefully in time obliterated. Remember no rx carries a 100% success. Thus far, microscopic varicocelectomy under experienced hands still comes up the best possible result.