Electricity is simply a flow of electrons between potentials (voltages). "Earth" is referred to as 0V to make for convenient notation. The "earth" provides an infinite source and sink for electrons (whichever is needed). Basic electronic theory does not allow for electrons to "build up" anywhere, and they always have to be moving. Considering these two facts, you have to have a place for electrons to come from and for them to go - this is earth. A point that, for basic circuit analysis, is infinitely conductive and is thus always at the same voltage.
And yes, your idea with the light bulb and the battery will work, as long as your "earth" is an ELECTRICAL earth (this means it is very very conductive). If you just shove two wires in the dirt it may work and it may not, depending on the dryness of the soil and mineral content and such.
Earth is used in mains AC powered devices for protection (the third prong of the plug is earth). basically if a high-voltage part of the circuit touches the metal case of the device, all the current will flow into the earth connection (infinite current sink) since the metal casings are connected to this third prong. This will prevent you from getting shocked if you touch the metal case while it is malfunctioning.