ground is, literally, the earth. At the electrical power generating station the neutral (zero volts reference potential) terminal of the generator is connected to a well-earthed point (e.g. Buried electrode). But remote from the generator the neutral wire may be several volts different from true earth potential because of stray currents in the wire and it can also have voltage spikes from interference. Isolation of as much of the circuit as possible from mains and neutral wiring is advisable to protect against shock/damage. You can't rely on the domestic neutral being at zero volts; some idiot may have connected wires wrongly at some point in the distribution system, or a cable may have been damaged and shorted.
Here's a circuit variation for a delta-wired system, avoiding the need for a neutral connection. Be aware that the voltage between phases is very high and the resistors and capacitors used at the inputs of the opt-isolators must be rated accordingly. these mains voltages are lethal. Due care must be taken. If in doubt consult a local qualified electrician.