The "presumption of innocence" is a fundamental part of our legal system in the United States. It means that a court will not perceive you to be guilty unless you are proved to be so beyond a reasonable doubt. In this respect, it's up to the prosecution to present facts and evidence that prove you to be guilty.
The presumption of innocence doesn't mean you can completely relax if you've been wrongly accused of a crime, but it does mean that the prosecution will have a harder time convicting you of a crime.
More about the presumption of innocence
As the cornerstone of our legal system, the presumption of innocence puts the responsibility to prove guilt onto state prosecutors during criminal proceedings. They must, beyond a reasonable doubt, show that you affirmatively committed the crime.
Without the presumption of innocence, defendants would be held responsible to constantly prove that they did not commit the crimes prosecutors accuse them of. With the presumption of innocence, incentive exists for prosecutors to only bring forward allegations for which sufficient proof exists to result in a conviction.
Interestingly, as a result of the presumption of innocence, defendants do not even have to say anything at all. Potentially, a defendant could remain silent and if the prosecution cannot prove the crime took place with sufficient evidence, the charges will fall flat and the judge or jury will issue a verdict of not guilty.
Simply remaining silent might not be the best idea
While defendants do have the right to remain silent, they also have the right to a criminal defense. In most cases, it's a good idea to exercise this right to a defense during criminal proceedings. For example, defendants can present evidence and arguments that cast doubt on the prosecution's line of reasoning. By illuminating more doubt like this, defendants may have a better chance of receiving a verdict of not guilty.
If, however, the evidence against a defendant is particularly strong, then the defendant might try to negotiate a plea deal in exchange for a less severe punishment.