The moistening of the mid-atmosphere is a very important process in hurricane development. Important enough that this next page will be dedicated to the understanding of the process.
You may wonder why we need to moisten the mid-atmosphere in the first place, it is the tropics isn't it? Well what do you think?
With cold air below and hot air above, this inversion inhibits convection because cold air is less bouyant than warm air, so any surface air that is lifted comes right back down and nothing happens. The next question you may ask then is: How do you get convection started at all then? Well, the inversion weakens on the western side of ocean basins and is its strongest on the east side of basins. This weakening in the west allows us to break through the inversion in places and features such as the monsoon trough and old fronts are strong enough to break the inversion and get convection started.
Getting the convection started is only half the picture in hurricanes though, we still have that dry air to deal with. But why is the dry air a big deal anyway, we got the thunderstorms going who cares if the upper air is dry?
Well, what do you think?
Dry air gets entrained (mixed with) the moist air and decreases the moisture content of the air. Less moisture content means less latent heat release, means the air is not warmed as much and the air more quickly becomes more dense than it's surroundings and sinks. This leads to less vigorous convection.
As we now know latent heat release is the life blood of a hurricane. Anything that limits or weakens the latent heat release, limits or weakens the chance of a hurricane. Dry air also leads to more evaporation in downdrafts, evaporation takes heat from the air its in, just like condensation releases it. Colder air can coexist with less water vapor than warm air. Therefor, dry air leads to colder downdrafts. This in turn leads to less water vapor in the air being taken up by the updrafts. This then leads to less latent heat release which, of course, is bad for the storm.
These two processes, along with the trade wind inversion is why moistening of the mid-atmosphere is so important to hurricanes. The entrainment process is the more important of the two as the downdraft effect may or may not actually lead to colder downdrafts.