... have naff all to do with static electricity.
Your skin is somewhat conductive. This is why you get a shock if you stick your finger in a mains socket. Don't try this, just take my word for it.
If you take an ohmmeter and grab hold of the probes, you'll see that you can measure this resistance. Depending on the size of the contact area (quite small in the case of the meter probes) you might see it go from anything from a few hundred thousand ohms, to about 1000 ohms.
Now, if you touch two points in the circuit, you are applying this extra resistance, just like if you had an actual resistor in there. Depending on how hard you press your finger onto the contact points, you can vary the resistance. Get an ohmmeter and try it - the harder you press, the lower the resistance.
The other thing that happens is that your body picks up electric fields from wiring, radio transmitters and all sorts of other things around you. You act as a big aerial. You're conductive, remember? This means that when you "buzz" the input of an amplifier you couple some of this electricity into its input. Mostly, what you'll be picking up is 50Hz mains hum from the wiring around you (or 60Hz, if you're in the US. 40Hz dropping to nothing, if your generator just ran out of diesel.) which is then amplified along with all the other noise and comes out as that familiar buzz.
So now you know.