Most circuits will function perfectly OK if they are grounded or not. Actually connecting something to the sand in your garden is very rare ... but see the note about mains operated equipment below.
The grounding usually shown on diagrams shows a point on the circuit which could be touched by humans without upsetting the operation of the circuit.
If circuits have to be connected together (like a preamplifier being connected to a sound system amplifier) then it is safe to connect the ground points on each circuit to the same point on the other circuit. In this case, the connection may be done with a shielded wire and the shielding is connected to ground at each end.
Mains operated equipment that has exposed metal parts should have the metal parts isolated from any internal voltages and must also connect to actual ground via the power outlet and the building power control board (switchboard). This is a safety precaution so that if there is some failure inside the appliance that would otherwise cause a risk of electric shock, current flows to ground and this causes a circuit breaker to activate or a fuse to blow. Either way, the power is removed from the appliance.