It's so inexpensive for what it covers that for me it's a no brainer really.
It basically covers any third parties for any damage you may cause to them whether that be corporal or material.
Some examples :
i) The flooring in your rented apartment belongs to your landlord.
You scratch/dent/ruin it - your liability will cover it.
ii) You go to visit a friend and spill a cup of coffee over his/her brand new computer/TV/camera/kindle and ruin it.
Your liability insurance will cover the cost of a new computer / TV / camera / kindle for your friend.
iii) You're going skiing and you'd like to film the lovely Swiss mountains so a friend lends you his/her video camera.
You break it.
Your liability insurance will pay for a new camera for your friend.
iv) You're cycling and you run someone over.
Your liability insurance will cover any damage caused to the person and his/her belongings.
---
In all of the above examples, if you damage your own property, your liability insurance won't cover it.
e.g. you drop your iphone and it breaks = not covered
you drop your mate's iphone and it breaks = covered
Just a couple of pointers :
i) When you ask an insurance company directly, they sometimes sign you up for 10 years
Make sure you sign for 5 or less.
Remember that if you leave Switzerland for good before the end of your policy, you can cancel your policy for the day you leave - you won't be asked to pay the non-used years or anything like that.
The advantage of signing for several years is that they cannot increase your premiums and if they do - you can leave.
ii) 9 times out of 10, they will put a deductible on it.
For the difference in premium, it's often not worth it.
The deductible is often 200CHF and a lot of claims may be under that amount so you may as well take a policy with no deductible so that if you do have to claim you're ok.
---
Hope that clarifies it a little?