Hybrid cars have petrol engines but also the capacity to run using a battery-powered motor. This means you have the benefit of the extra power that a petrol or diesel car engine provides, ready to use as and when you need it, but in an altogether more environmentally friendly vehicle. It also means you're less likely to be caught short between electric car charging points which, although increasingly common, aren't available everywhere quite yet.
Insuring a hybrid car is much like insuring any other, with prices varying accordingly. Some of the most popular models, like the Toyota Prius or BMW i3, rate highly for safety as well as efficiency though, and so are generally cheaper to insure than many petrol cars.
Hybrid vehicle drivers enjoy a limited version of many of the other benefits that EV drivers do, including reduced road tax and, for those who live in London, reduced congestion charge fees.