When someone asks you for something and you say NO, you're refusing. To refuse is to say "No." You could refuse by saying "No, I won't do that," or "No, I don't want to do that," or "No, you can't have that."
If I ask, "Would you like some spinach?" and you say "No, none for me," then you've refused the spinach, and you've refused my offer of spinach.
Refusing is a very strong, very firm action. Still, it can be nice and polite. If I tell you, "Please eat some spinach," and you say, "No, thank you; I have plenty of other things on my plate to enjoy," then you've refused politely. You gave a polite refusal. But if I tell you to eat the spinach and you say, "Absolutely not. I will never eat it. You can't make me! Get that vile vegetable away from me!" then you've refused quite rudely. You gave a rude refusal. Chill out!
Even things seem to refuse to do what you want. Your computer might refuse to work properly. On a rainy day, the sun refuses to shine. And very sticky stickers might refuse to come all the way off your desk.
Refusing can be rude, but it can also be an excellent idea and a wise, brave move. If a friend wants you to help him steal something and you refuse, good for you! If a classmate says you're stupid and you refuse to believe her, good for you! If a neighbor asks you a rude question and you refuse to answer it, good for you! If a boss tells you to work extra hours for no pay and you refuse, good for you! Stand up for yourself, and refuse whatever needs refusing.
One more thing! Take a close look at the word "refuse." The re part means "back," and the fuse part more or less means "give," which makes sense because refusing things can mean to give them back: to say, no, take this back, I don't want it. Keep that in mind when you notice that there's also a noun, "refuse," spelled the same but pronounced differently. Refuse is trash, or garbage: it's stuff that you throw away. For example, when you go camping, don't leave any refuse behind: take all your trash with you. And for another example, a refuse company hauls away your trash: all the stuff you want to throw away.