Aansprakelijkheidsverzekering (private liability insurance) is close to standard in Dutch households and almost unknown to people who have just arrived, since nothing in the registration process prompts it. Plenty of tenancy agreements now list it as a condition, which is how many newcomers encounter the word at all.
Not legally, no — but treat "not required" as a technicality rather than a reason to skip it. It typically runs somewhere around €3 to €8 a month depending on whether you're insuring just yourself or a whole household, and it covers damage you accidentally cause to other people or their property: your kid breaks a neighbor's window, your bike takes out someone's car mirror, your dog knocks over an expensive vase at a dinner party. Without it, you're personally on the hook for the full repair or replacement cost, which for anything involving injury or serious property damage can run into tens of thousands of euros. It's close to universal among Dutch households for exactly that reason, and plenty of landlords now write it into the huurcontract as an explicit condition of renting, alongside contents insurance. This is general information, not a recommendation of any specific insurer or policy — compare coverage limits and excess amounts across a few providers before picking one, since €2.5 million liability coverage is fairly standard but the exclusions differ more than the headline premium suggests.