You could almost explain it with that cool avatar!
As electrons leave the cathode and sail towards the positive plate, some of them "leak" onto the grid wires which are in between the cathode and plate. If you use a big enough resistor from grid to ground, you can keep these electrons "trapped" on the grid. That is why typical grid to ground resistors in a grid leak circuit are usually 5 to 10 megohms. If you can collect enough of these electrons on the grid, they will form a negative charge large enough to bias the tube, which will keep the plate current where you want it.
Measuring bias volts on a grid leaker can be tough without a vacuum tube voltmeter, as the voltmeter's internal resistance can bleed off some of the electrons, giving you a lower than normal reading.
Grid leak bias is sensitive to the surfaces of the tube elements. This is why only a handful of tubes are usually good candidates for grid leak usage. So I guess you could say that it is kind of a touchy way to bias a tube. I believe that as a tube ages, it's grid leak bias may change more than a cathode biased tube. But, grid leak bias tends to produce lower distortion if the plate current is kept down to 1 ma or below.
The bias voltage of a tube used in grid leak mode will generally be between 0.1 volts and 1.1 volts, depending on the tube, and this bias may change as much as 0.4 volts during the life of the tube.
In a typical cathode bias circuit, the grid resistor is usally around 100 K to 1 Meg, which lets any electrons picked up by the grid flow back to ground.
I believe fets can display this same grid leak phenmenom, but I forgot how. I guess electrons getting to the gate somehow and not having a way to get back into the Drain Source channel.
I believe grid leak got it's start in the IF sections of radios.
It is used with other tubes, but mostly in the early days of guitar amplifiers. Noise and hum are sometimes a problem with grid leak bias. You can get away with a grid leak guitar amp at home, and maybe at a house party, but if you take it down to Jam Night at the local club, you will be in for a rude awakening, due to stage lights making your amp sound like a Kenworth hitting the jake brake coming down the grapevine. In order to keep the complaints down, Fender and others moved away from grid leak and over to self or cathode bias.
Some people complain about a lack of headroom with grid leak bias. This might be because typical bias voltages with grid leak are usually lower than a typical cathode bias voltage. I have two amps that use grid leak, one is a Vox AC-15 circuit that grid leaks an EF-86, and the other is a Champ circuit that uses a 6SJ7 metal tube in grid leak. I have no headroom problems, even while using stomp boxes. I like the mellow tone of this bias technique as opposed as to you garden variaty 12AX7a/1.5K input stage.
Grid leak bias tends to give you a warm, compressed sound. My guess is that this is due to the fact that as the signal to the grid increases, more electrons flow to the plate, which means more electrons hit the grid, which means more negative bias, which means less plate current. So there is kind of a self limiting thing going on.
cj