A wet proof is a proof print used in the printing industry.
Whereas a regular proof print is usually done on an industrial laser printer (also known as a Laser Proof or sometimes as a Dry Proof), a wet proof is the step up from a laser proof: Instead of making an approximate of how the final printwork will look, the actual print plates are made, and an extremely low print run (typically 4-5 prints only) is made, to see how the final result will look. If the customer decides to accept the proof, the same print plates are used to make the final print run. If the customer declines to accept the proof, alterations have to be made to the design (or, more frequently, colours need adjusting), and new print plates will have to be made.
Anyone who has had any dealings with printing will tell you that the most expensive part of printing isn't the paper or inks, or even the time the actual printing takes, but the making of the print plates, because it is relatively skilled and labour-intensive work that has to be done by (skilled) human beings. Because of this, a wet proof is rather expensive, but it is cheaper than having to reject a print run of a million flyers, because the colours are off, or there are last-minute alterations that need doing.
Wet proofs are usually done on full pages or full publications only. While it is possible to do a wet proof on an element of a page (such as an advert or a single picture, for example), part of the point is lost, as new print plates will have to be made to print the actual page.