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Let's say village A has all the something S they need, and village B has all the something T they need. The properties of S outweigh the benefits of T.
Village A and village B start to trade S for T.
After trading, is the value V of S + T now different?
The net value of the two villages increases because value is in the eye of the beholder. If commodity S is more valuable to village A than to village B, and commodity T is more valuable to B than A, then, when they trade, both villages gained something of more value to them and the relative wealth of both villages increased.
Value comes from the valuator.
This is why--one of the reasons, anyway--Marxism was doomed. Value doesn't come from labor at all. Only cost comes from labor. For example, if I go stand in the middle of the road and labor all day pointing at the sky, I've worked hard but created no value, because no one else values my sky-pointing. Similarly, if I build two houses and put exactly the same amount of labor into both of them, but one is on a mountain with a beautiful view of the city, and the other is next to the city dump, the first will be far more valuable because people would value the location of the first, "envaluating" the house.
The example by @CWill is correct in an exchange economy (explore more of it here), but does not apply to a production economy.
As David Ricardo explained, the only condition needed for exchange is the existence of comparative advantage. This is when say group A is relatively more productive in the production of one good than another group B. Then, group A will specialise in the production of that good, whilst group B will specialise in the other good. Trade will expand the overall production possibility frontier, which means consumers in both groups will see an expansion in their consumption possibilities. Thus, through trade, they can both consume more. Importantly, this is independent of any different in consumption (actually, trade still occurs if preferences are identical). The role of preferences is to determine the relative prices of the goods.
Notice that one reason why a group might have comparative advantage is relative abundance. For instance, one country might have a sea with so many fish that, even if using a net of the same size than another group, the output of such fishing will be very high. In this case, relative productivity is different between groups; comparative advantage exists.
Another nice example is that of Robinson Crusoe's economy.
