If a meter is connected to an inverter, it will measure the number of kilowatt-hours produced by that inverter.
Typically, meters are wired between the service entrance and the main service panel, and they indicate how much power the house has used. Utility companies use meters to figure out how much to bill you.
The meter in this picture is a "Net Meter." Note the red sticker on the bottom right. Also notice that there is an arrow pointing to the left, underneath the number "4" on the LED screen. This is indicating that the meter is actually running backwards, counting down the number of kilowatt-hours that the house has consumed. In effect, Net Metering is a way to get your utility company to buy your clean power. Many homes do this.