What is Copper Thieving and why use it?
Unfortunately the other 3 answers to the question are incorrect, but helps keeping a common misunderstanding alive :-)
Thieving is added to the outer layers in order to help a more balanced chemical process for the plating.
Also notice that there is no need to "balance copper" (or stackups for that matter) in modern PCB fabrication to avoid "warped boards".
I wrote about this on my blog recently. You can find other references on the net.
Copper dots (or grid/solid fill) are used mainly to balance the thermal properties of the board, to minimize twist and warp as the board goes through the thermal cycling associated with reflow and improving yield.
A secondary purpose for them is to reduce the amount of copper that needs to be etched away from the board, balancing the etching rates across the board and helping to make the etching solution last longer.
If the PCB designer did not explicitly "pour" copper fill into the open areas of the board's outer layers, the fabrication house will often add the small disconnected dots, because these will have the least effect on the electrical properties of the board.
In general, it is better for the manufacturer when less copper have to be dissolved during the etching process and there is no big continuous areas that need to be etched. It is because of 2 reasons:
Etching more copper means that the etching solutions have to be recycled more frequently - it is an energy and money. An ideal case is if the customer wants a PCB entirely covered with copper. :)
The big solid areas of copper are etched slower than the areas where fine copper pattern is located. That is because the pattern has bigger surface and we know that the chemical reactions speed is bigger if the reaction surface is bigger. This way, after the tracks are already fully etched, the big empty areas are still not, so the PCB have to stay some more time in the solution. This causes some under-etching of the tracks which is not good for the PCB quality because it makes the tracks thinner than intended.