There are several types of hybrid cars:

The most common one is where they are powered by the engine in high speed-high load conditons (motorway) and then use the electric motor for low speed low load conditions (city).

What you are referring to is a full hybrid/electric car which has no engine, hence the need for it to get charged. Some power stations will soon be 100% emissions free and will be the source of this electric power, but this costs a lot of money and governments are yet to fully pledge towards the costs!