Sound is a pressure wave. Continuous sound is a continuous stream of high pressure fronts followed by low pressure fronts. The louder a given sound is, the higher the difference in pressure between a crest and trough; pressure is the amplitude of the sound wave. Furthermore, the volume of a sound is also dependent on frequency. Humans are not as sensitive to high frequency and low frequency sounds. So, for example, a song with a lot of bass has to be played at a higher amplitude in order to be just as loud.
The threshold of pain (that is, the loudest a sound can be before most people experience pain) is about 100 phon. The figure below from Wikipedia shows how that relates to amplitude and frequency.
The red lines show constant volume. The abscissa is frequency and the ordinate is sound pressure level.
As you can see, for 100 phon, the low frequency sounds go up to $130$ dB. I'll spare you the explanation from Wikipedia, but this translates to the high pressure fronts being about $150~Pa$ above the standing air pressure and the low pressure fronts being about $150~Pa$ below average. That means from high to low pressure, you experience a $300~Pa$ difference. That may not seem like much given that the sea level pressure is around $101~kPa$, but it should be noted that $100~Pa$ is the pressure from a strong breeze and $300~Pa$ is about the lung over-pressure of a normal breath. So it's not surprising that you feel a pulse every time the music plays a strong bass. Another way to look at it is it's like you're lying down and every time a bass note is played, your whole body is covered with 2 layers of US quarters, which are removed once the note stops again. Doesn't sound like much, but you'd definitely notice it.