GFCI recepticals are kinda similar to a breaker in your breaker box. The difference is that breakers trip when there is an overload. GFCI's trip as soon as a path to ground is identified (ie, a person getting shocked by stray voltage).
A ground probe is simply a titanium or stainless rod with a wire connected to it and the wire is connected to ground. This allows any stray voltage to go directly to ground, which in turn alerts the GFCI that ground has been found and the GFCI trips.
Otherwise you would have to put your hand in the tank, let the electricity travel through you to ground before the GFCI trips. Which although it sounds rough isn't bad at all and it will save your life in the case of a severe voltage leak.
The reason you can't use a probe without a GFCI is this.... ok, say you have a voltage leak in your tank. The ground probe is absorbing all of it and taking it to ground. Ok, so then you put your hand in the tank and for some reason (ie, wet bare feet, hand on metal...etc) you become a path of least resistance for the stray voltage. So instead of making it's way through the ground probe it finds an easier path to ground through you. No GFCI means no tripped circuit..... means bad shock and/or death to you in some cases, although rare.