Water activity, written a-w, is the ratio of the vapour pressure of water in a product to the vapour pressure of pure water at the same temperature. It runs from 0 to 1 and measures the water that is actually **available** to micro-organisms and to chemical reactions.
Moisture content, by contrast, measures **total** water, including water bound to sugars, fibres and proteins that nothing can use. That is why two products with identical moisture content can behave completely differently in storage: the one with more sugar binds more of its water and sits at a lower water activity.
Microbial growth thresholds are expressed in water activity for this reason. Bacteria need the most available water and stop first, yeasts next, moulds next, and the xerophilic moulds and osmophilic yeasts that spoil under-dried high-sugar products tolerate the least. The exact threshold depends on the organism, the temperature, the pH and any preservatives present.
Two practical rules. Always state the measurement temperature, because water activity is temperature dependent. And remember that the value you shipped is only maintained by the pack: a porous product in a permeable film will drift upward until it equilibrates with the air around it.