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Sound Waves In Scientific Language: The following animation (Fig 1.) shows the difference between the oscillatory motion of individual particles and the propagation of the wave through the medium (gas, liquid or solid).

Notice how the particles move backward and forward around a fixed point: The 'wave' effect travels (note the black arrow), but not the particles themselves (note the red dots and arrows).

The animation also identifies the regions of compression and rarefaction.

Fig 1. Longitudinal Waves (sound) - particle movement & wave propagation

More scientific explanation of sound waves is available at The Physics Classroom

How Do Heat & Sound Interact

Why is sound absorption in water less than in air? According to my text, for a 1 kHz signal in water the loss by medium absorption is about 0.008 dB/100 m. In air, the loss is much greater: about 1.2 dB/100 m.

Imagine that we could take a very fast picture of certain properties of a sound wave during transmission. The pressure varies from a little above atmospheric, to a little below and back again as we progress along the wave. Now the high pressure regions will be a little hotter than the low pressure regions. The distance between two such regions is half a wavelength: 170 mm for a wave at 1 kHz in air. A small amount of heat will pass from hot to cold by conduction. Only a very small amount, because, after half a cycle (0.5 milliseconds for our example), the temperature gradient has reversed. Although it is small, this non-adiabatic (non-heat conserving) process is responsible for the loss of energy of sound in a gas.

What happens when we change the frequency? The heat has less distance to travel (shorter half wavelength), but less time to do so (shorter half period). These two effects do not cancel out because the time taken for diffusion (of heat or chemical components) is proportional to the square of the distance. So high frequency sounds lose more energy due to this mechanism than do low. This, incidentally, is one of the reasons why we can tell if a known sound is distant: it has lost more high frequency energy, and this contributes to the 'muffled' sound. (Another contributing effect is that the relative phase of different components is changed.)

So, let's now dive into the main question. Three different parameters make the loss less in water.

  First, sounds travels several times faster in water than in air. (Although the density of water is higher by a factor of about 800, the elastic modulus is higher by a factor of about 14,000.) So, for a given frequency, the wavelength is longer and the heat has further to travel.
  Second, the water does not conduct heat so rapidly as does air. (This may seem odd if you've recently dived into cold water, but the effect in that case is largely due to water requiring more heat for the same temperature change. Not counting the fact that you probably wear more clothes when out of the water.)
  Third, the temperature of water rises less under a given imposed pressure than does that of air. 

All three effects go in the same direction, and their cumulative effect is substantial, as your text's values suggest. Source - http://newt.phys.unsw.edu.au/jw/musFAQ.html#absorption