You have been paying your monthly LAMal premium for months. One day you have to go to the doctor, nothing serious. The following month an email arrives from the insurance company with the details of expenses. And you find that they haven't paid anything, because you haven't covered your franchise yet.
The franchise is the annual amount you pay directly before the insurance starts working. In Switzerland you can choose between 300, 500, 1000, 1500 or 2500 CHF per year. If you choose the high franchise, your monthly premium goes down quite a bit, but you assume that cost if you need medical attention. If you choose the minimum of CHF 300, the insurance starts earlier, but you pay more each month. The logic is clear once you understand it.
What many people do not know when they arrive is that there is a second mechanism: the quote-part. It is 10% of all expenses once the franchise is covered. That 10% has a ceiling: 700 CHF a year per adult, 350 CHF per child. So in the worst of years, if you have the maximum franchise, the maximum you can pay out of pocket between franchise and quote-part is CHF 3,200 per adult, in addition to the monthly premiums.
Many people choose the high franchise upon arrival because the monthly premium seems more manageable. And it makes sense if you're young and not going to the doctor. The year you have an operation, a hospital stay, or just several visits in a row, the numbers suddenly change. The surprise is always the same: they thought that insurance covered everything from the first franc. In Switzerland the theory is much more complicated than that.