What makes the buzzing sound when touching an audio line?

Your body becomes connected to the circuit. Probably, capacitively coupled through an equivalent of about 100pF. Then, several things can happen:

• Extra capacitance makes your amplifier oscillate.

• Your body acts picks up 50/60Hz interference from power lines (aka "60Hz hum") and introduces it into your amplifier. To see this, poke an oscilloscope probe at yourself and observe the signal.