I recently built an audio amplifier based on the LM386. When I touch one of the input signals with my finger, I can hear a buzzing sound on the output. I checked with the oscilloscope, and there appears to be some kind of voltage signal on my hand with respect to the amplifier's ground. What is this voltage? By what theoretical principle can I understand this?
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.
Your body is acting as an antenna, or more accurately, the secondary winding of a transformer. A tiny AC voltage/current is being induced in your body from the electromagnetic field produced by the mains electricity power lines all around. When you touch the input line of an amplifier, the tiny voltage/current is amplified and a 50 (or 60) hz sine wave is produced at the amplifier's output. This causes the speaker cone to push and pull 50 (or 60) times a second, producing the hum you hear. Anything that can act as an antenna (or transformer secondary), whether your body or a piece of metal or a length of wire, will have the same effect.