Sound waves are longitudinal waves which can travel through any material—solid, liquid, or gas—but not empty space. As you can see from the animation, as the molecules move back and forth, there develop these regions where the molecules are much closer together (areas of compression) and other regions where they are farther apart than usual ( rarefaction). Thus it is common to think of these as "density waves" or pressure waves (see Pressure for a review).
As mentioned in Wave Pulse, sound travels faster in solids than in air, which is why you can hear a train coming by putting your ear on a railroad track (please don't do this!) before you hear it through the air. Even in air, the speed of sound depends somewhat on the temperature. At room temperature (20°C), it moves at 343m/s; at 0°C, on the other hand, it drops down to 330m/s.
Our ears interpret the amplitude of a sound wave as its loudness (see Decibels), and the frequency of a sound wave as its pitch: high-pitched sounds have a higher frequency than low-pitched sounds. Human ears are said to be able to hear frequencies between 20Hz and 20,000Hz, although this varies from person to person, and people tend to lose the higher frequencies in particular as they age.
Most sounds we hear are actually made up of a number of different frequencies at once: the lowest or fundamental frequency, and then a series of overtones, which are higher frequencies which sound at the same time. The proportions of these overtones is what gives sounds their timbre: it's what makes a piano sound different from a trumpet, for instance, or the vowel "E" sound different from the vowel "O".