When you rent an apartment in Switzerland, most contracts include a clause that requires you to have home contents insurance. In French it is called "assurance ménage", in German "Hausratversicherung". Many newcomers sign it without knowing exactly what it covers, and others don't directly hire it because, unlike the health box, it's not required by law. That is, except in four cantons: Vaud, Freiburg, Jura and Nidwalden, where fire and natural damage insurance is legally enforceable.
What this insurance covers is simple: your stuff. If there is a fire, flood, burglary, or storm that breaks windows and wets the living room, insurance compensates you for the value of what has been lost or damaged: furniture, clothing, appliances, computer, bicycle, sports equipment. What is not covered, unless you expressly add it, are the damages that you cause to third parties or to the apartment itself, which is what private liability does. That's why many insurers sell the two in the same contract.
The price varies depending on the coverage and the canton, but we are talking about 100 to 200 francs a year, sometimes less. It's not a figure that ruins anyone. What can ruin someone is discovering that their laptop, furniture and all their clothes were destroyed in a fire and that no one is going to pay them anything because they did not take out insurance. Many people discover that too late, usually the first time something goes wrong.