The watch is a tracking or spy device of some sort.
The watch is connected to the Watch that Mr. Paik gave to Jin, implying a pre-Island connection between Christian and Mr. Paik. Perhaps Christian gave it to Jack and told him that story knowing Jack would make the opposite choice Christian did.
The watch is somehow representing or related to the interesting time phenomena of the Island. It is either just a symbol or it will be very significant when fixing the time travels seen on the Island. The watch being an heirloom also supports the theory that the Shephards (at least Christian and Christian's father) have been related to the island for a long time.