A prominence is a relatively cold, dense structure suspended in a thinner and very much hotter environment. This goes against our normal experience. Hot material rises, cold material sinks, so something must be holding these prominences up.
What’s more, if you put a cold object next to a very hot object, the cold one usually heats up very quickly. It’s as if the prominence is taking a rest in a cool hammock above a roaring fire, without even getting warm!
There’s good evidence that the Sun’s magnetic field is the key to all this. Here’s an experiment you can try yourself. It shows the principle behind one possible explanation for pominences.