Dried fruit and nuts are sometimes consumed together as a whimsically-named product: "trail mix". That's not the only reason these two products fall in the same category on this web page. Both dried fruit and nuts are natural products that usually undergo post-harvest processing before they are sold to customers or consumers. Moisture mistakes for both these product categories are similarly painful: too much water means mold; too little means lost profit, not to mention quality issues.
Most growers or buyers use moisture content to determine if tree nuts or dried fruit are too "wet". This can cause problems. First, the moisture level that causes mold is different for every kind of nut or dried fruit. Second, loss-on-drying moisture isn't a very precise method for measuring moisture - the answer you get depends on the method you use.
Water activity is different. It's a snap to identify bad batches that could mold: any product over 0.7 aw can mold, anything under that value won't. It doesn't matter what your product is. Using water activity as a standard can eliminate the guesswork over whose moisture meter is right. Two water activity meters measuring the same sample will give the same reading. If you really want to know your moisture content, a new version of AquaLab can give you both moisture content and water activity from the same reading.
Dried fruit and nuts last a long time on the shelf, but not forever. In the end, lipid oxidation and other chemical or enzymatic reactions make the product unpalatable. Because water activity is a measure of energy, it influences how quickly these reactions occur.