The burst pressure for a hydraulic hose is what the manufacturer offers as the maximum pressure before a particular hose will generally explode or have a rupture in it. Different hoses and hose styles will have different burst pressures; this will also vary somewhat between different manufacturers.
The entire hose is not necessarily going to explode catastrophically, like an exploding propane tank, but the nature of hydraulics and the bulk modules of oil mean that you’ll have a tiny pinhole and a squirt—and something will give way and allow pressure to bleed out or drop quickly. With a given hose, you might discover that the minimum burst pressure is exactly four times the maximum working pressure. In most cases, hydraulic hoses are rated on 4:1 safety factor. That’s the same thing for hydraulic cylinders, such as an NFPA cylinder. Typically, rated for maximum burst or fatigue strength is four times what your working pressure is, and manufacturers call that the safety factor.