The adverb impossibly describes something that's utterly unlikely, or that can't possibly be achieved. If a marathon runner becomes exhausted at a spot impossibly far from the finish line, she might never make it.
If you hold yourself to impossibly high standards when it comes to school, it means you'll never be happy with the grades you get. And if you see a girl with eyes the color of emeralds, you can say she has impossibly green eyes — in other words, it doesn't seem possible they could be so stunningly green. Impossibly, from the adjective impossible, has the Latin root impossibilis, "not possible."