Something obviously true is clearly, totally, unmistakably true. There's just no doubt about it.
Obviously is a word people use when they are sure of something and sure that it's plainly clear to others. When you get presents on your birthday, you're obviously happy. Dogs obviously like to chase squirrels. The sky is obviously blue. People also use this word when they're being mean or sarcastic. If you didn't know who walked on the moon, a friend might say, "Obviously, it was Neil Armstrong!"