Supercritical liquids are generally weird. H2O, for example, changes from being a polar solvent to a nonpolar solvent -- you can dissolve oil in supercritical water, and even burn it if you have a source of oxygen. It's also more corrosive -- which is relevant if you're considering using supercritical water in a nuclear reactor.
Easiest case of this: You have a tank of water and oil under supercritical conditions, and you pump high pressure oxygen gas into it. You get a "flame" around the intake, but unlike a regular flame (which is the boundary between fuel and the surrounding oxidizer) this is the boundary between the incoming oxidizer and the surrounding fuel.
The combustion products are the same as you would get in the absence of the supercritical water -- typically H2O and CO2 -- but they're all contained inside the supercritical water tank, which makes this very convenient for e.g. disposing of chemical weapons.
