On Grid Defined
Most solar power systems are on grid, meaning that they are connected through an electric circuit to the public power coming into the house. That is called the grid. When the sun is down the solar power is not there so the house is powered by the grid. When the sun rises and solar power builds up then the power used by the house is supplied by the solar panels and not by the grid. When power comes from the grid the power meter tracks the amount of power and adds charges to the power bill.
Net Metering Defined
Most public power companies offer net metering which is valuable to the homeowner because it reduces the power bill when the amount of solar power is greater than the amount of power the house uses. In that case, some of the power is fed back to the public grid through the power meter. The power meter effectively runs backwards, much like running a car in reverse to reduce the miles on the odometer. The power charges are reduced by the meter so the charges are the Net result of power coming in and power going out.
Off Grid Defined
The ideal solar power system is one that does not need to depend on any outside power source. It is capable of supplying all the power your home needs all the time. Since the sun goes down, power must be stored so it can be used when the sun is down. That is done with batteries just as a car battery stores power when the motor is off. When there is sufficient battery storage to supply power all the time the house can be disconnected from the public power grid. Hence the term Off Grid. Now, the fact is that it is not necessary to be off grid all the time unless the house is far from public power lines.