Whether gas, solid or liquid, the medium refers to the substance that supports the transmission of sound. For example, whales send signals over miles in the water, demonstrating that liquid transmits sound. Putting one's head to the ground, it's possible to hear a horse approaching at a gallop, demonstrating that solids transmit sound. Sound travels through the air (a mixture of gases -- nitrogen, oxygen, carbon dioxide and others) all around us all the time, which is an example that gas transmits sound.
Sound is transmitted by a high-pressure event that results in a low-pressure event. Imagine a rock thrown into a pond: The splash of the rock causes compression or high pressure in one area, and the resulting waves cause rarefraction or a low-pressure event in the surrounding water. The same effect happens whether in a gas, liquid or solid environment. These waves are then measured using the properties of frequency, wavelength, period (duration of wavelength), amplitude (height of wave) and velocity (speed of wave).
These are sound waves where the compression and rarefraction occur in the same direction the wave is moving. There are also waves in which the vibrations are perpendicular from the source; an example is those coming from a string on an instrument.
How a sound wave travels depends on the medium through which it is traveling. Depending on the material through which it passes -- gas, liquid or solid -- the sound wave will have different pressures and densities. The sound wave will also travel at different speeds depending on which material it is traveling through and the ambient conditions. Visualize trying to blow bubbles into water, smoke into the air or a hand hitting a bongo drum. The distance the bubbles, smoke or sound of the bongo drum travels will depend on the density, temperature and other ambient factors of the medium through which it travels.