Electric vehicles are powered entirely by — you guessed it — electricity. You can plug them into the wall like a smartphone or charge them using charging stations that draw power directly from the grid (or your home solar system, if you have one).
Hybrid vehicles are powered by two things: an internal combustion engine and an electric motor. The electric motor draws its energy from batteries, which are charged by the internal combustion engine and a process known as 'regenerative braking'.
Hybrids are (generally) more efficient than traditional vehicles — the electric motor allows for a smaller engine, while the battery reduces engine idling. That said, the internal combustion engine still needs fuel — petrol, usually — and its battery can't always be charged by a charging station.
This setup is different for Plug-in Hybrid Electric Vehicles (PHEVs). While they still have a petrol engine that can be used to charge the battery, they can also be charged using a public or home charging station.