What is the meaning of reconstituted juice?
What they mean is that they took some grape juice and concentrated it by evaporating some of the water contained in it (a concentrate is juice in which the sugar content is increased at least of 50%). 

This is good for producers because concentrated juice has a lower volume, is easier/cheaper to stock/transport etc.
When they bottle the juice, they then reconstitute it by re-adding the water to the concentrated juice.

24.7% means they originally removed 75.3% of the water to make the concentrate. Because they added it back, at the end you are back with reconstituted 100% juice.

EDIT: fruit juices are regulated by the Codex general standard for fruit juices and nectars (PDF) which lists the minimum Brix Level (=sugar content) for various juices. Reconstituted juices must oblige to these minimum standards, although local laws may vary.