Essentially, this means you are covered for accidental injury, death or illness to another person, or accidental loss or damage to material property. To put this into context, here are two examples of each type.
You are on an overland tour, and you pick up a pot of boiling water off the camp fire, realise it’s extremely hot and immediate drop it, but in the process of doing so you badly scold other travellers, which result in them becoming hospitalised and missing the rest of the trip. These other travellers will in all probability sue you for damages. That’s why you need cover for accidental injury.
The other example is that you’ve checked into your hotel in Penang after a day on the beach, and you start running the bath. You then go out onto the balcony to gaze across the sea, have a Gin and Tonic, and slowly doze off to sleep. The bath carries on running, overpowers the overflow, goes all over the floor, seeps over the carpets, then seeps through the floor and damages the room below. The hotel is going to want payment for all the damage, and compensation for the fact that will have to take two rooms out of service whilst the damage is repaired.
Note the Personal Liability cover will not cover you whilst driving a car, motorbike or any other type of machinery (for example Jet-Ski’s and the likes), as this will be covered by the relevant insurance for that, and nor will if cover you for taking part in any trade, business or profession.