These hoses are the flexible braided pipes under your sinks and vanities, or often run between your toilet tap and cistern. These pipes are relatively new additions in Australia (the last 15-20 years or so). They are much faster and cheaper to install, however these little pipes are supposedly the largest contributor to household insurance claims in Australia.
These Braided hoses only have a lifespan of around five years and are rated to 500kpa of pressure (many houses in Australia can easily exceed 500kpa). When the pressure is too high, then the hoses can burst. The best thing to do with these flexible hoses is to have them replaced every five years, and to have a pressure limiting valve installed to stop excessive water pressure in your plumbing.
These pipes should also always be installed with shut off or mini taps so that if the worst does happen then the water can be turned off very quickly. If you do these three simple and relatively inexpensive things, you will dramatically reduce your chances of a burst pipe.