A liability insurance is optional and it is considered to be one of the most important voluntary insurances. A liability insurance covers the costs when you damage something that belongs to another person or do someone an injury. For example, they cover the damage if you scratch someone's car while riding your bike. Same applies if you cause an accident and the injured individuals demand you to pay their medical costs and compensate for the pain you have created them. This can be very expensive, and without a liability insurance, it may make your life really difficult.
Besides, the liability insurance can provide you with legal protection, in case someone asks you to cover damage which, in fact, was not caused by you. Your small pets and children will be also included in the liability insurance. So if your child, for example, breaks another kid's toy, your insurance can pay for it. For larger animals, e.g. big dogs and horses, there is a separate type of insurance called "Tierhalterhaftpflicht".
You can decide about the amount of insurance you are buying. The German Consumer Center ("Verbraucherzentrale") recommends a liability insurance as big as at least 5 million euros. After deciding about the insurance sum, the outlay of contributions will be determined. With a 5 million Euro liability insurance, you would have to pay about 50 to 80 euros per year. The Consumer Center explains the liability insurance system in this video, and they can also provide you personal counselling.
At Vergleichportal Check24, you can compare different liability insurance schemes and choose the one that fits your needs.