Something that's impossible can't be done. If you want to stop eating donuts but you just can't, you might say it's impossible.
If it's impossible, it cannot happen, or it doesn't exist. You might wish you could bring Abraham Lincoln back to life for a day so he could come to tea, but that's impossible. People use the word impossible to mean "out of reach" or "too hard to achieve." A terrible situation can be impossible, and so can a person who refuses to compromise or seems intent on making things difficult for everyone else.