here you go:
When a voltage is applied to the gate of the transistor, it acts as a capacitor and builds charge, inducing a charge in the bulk of the silicon and inverting its type (positive voltage to an NMOS gate inverts the p-type bulk silicon to n-type as electrons build up near the surface). In a flash transistor, the floating gate builds up the charge by attracting electrons out of the silicon through the oxy-nitride gate insulator -- in NAND flash, the electrons are transferred to the gate by tunneling (see wikipedia, quantum tunneling), and in NOR flash the electrons transfer to the gate by the hot electron effect (that is, give the electron more potential energy than the oxy-nitride band gap -- think of it as jumping over the insulator in 4-d space, the 4th dimension in this case being energy). In order to remove the charge on the floating gate, a negative voltage must be applied to the primary gate to repel the electrons and give them the necessary energy to transfer out of the floating gate -- otherwise the electrons won't be able to go anywhere. This is how you write a bit (or set of bits, if you do different voltages and timings) on a single flash transistor. The fact that the electrons can't go anywhere without an applied voltage is why the stored values remain after the power is out.