Firn is a word used in both Swiss and German to mean 'old' or 'last year's'. It has entered the English language in only one very specific usage -- it refers to last year's snow. Firn is snow that has lasted through the summer, and especially snow that can be expected to last through many summers. Firn is permanent snow, snow that may slowly be built upon and, perhaps, eventually turn into glacial ice.
Spiegel is the German word for mirror. While spiegel is usually used in English to refer to pig iron with a high percentage of manganese, in the case of firnspiegel it is simply referring to a reflective brightness of the snow.
Firnspiegel, AKA glacier fire and firn mirror, refers to an icy crust that forms on snow that has survived the summer, but due to a slight melting and refreezing has become reflective and mirror-like. It forms when the air temperature is below freezing, but the surface snow retains enough solar energy to melt slightly. After the initial ice layer forms, it will help to trap solar radiation more effectively, and may melt snow out from under the ice, resulting in an air gap between the firnspiegel and the underlying snowpack.
Firnspiegel ice is very thin, and the snow below it generally makes for great skiing. The ice will not interfere with the skis, but will break and fall away with a light tinkling sound. Firnspiegel's reflections can be impressive, but are not strong enough to cause snow blindness or other major problems. It's just pretty, that's all.