What is a crime? It's an act or omission prohibited by law for the benefit of the public. Violation of these law is prosecuted by the government and can result in imprisonment, restrictions of liberty or fines.
What if the victim doesn't want to press charges? Can the case be dismissed, maybe not, because the District Attorney's office represents the state decides what cases to prosecute as crimes and does not need the permission or consent of the victim of the crime.
What are the types of crimes? Felonies and Misdemeanors. Felonies are crime that can result in prison. Misdemeanors are all other type of crimes that can result in fines and time in the county jail.
Crimes can also be classified as Malum in Se and Malum Prohibitum. Malum in Se, mean that something is wrong because it it bad, immoral, or dangerous. For example Murder is a Malum in Se crime. Malum prohibitum means that something is illegal only because the law makes it wrong. Speeding is a Malum prohibitum crime.
Burden of Proof, who has to prove you committed a crime? The state or the government, represented by the District Attorney's office must prove that a crime has been committed and that you were the person who committed the crime.
Under the 6th amendment a defendant has a right to a jury trial where all the elements of the crime must be proven beyond a reasonable doubt.
1 In re Winship, 397 U.S. 358 (1970)
2 Sullivan v. Louisiana, 508 U.S. 275 (1993)