A felony is any serious crime according to a country's laws. This would include murder, of course, but also includes things like robbery (especially armed robbery) of a large amount of money, burglary and kidnapping, among others.
A person who commits a felony is a felon.
Less serious than a felony is a misdemeanor. Misdemeanors include begin drunk in public, littering, creating a public disturbance and getting into a fist fight. A person committing a misdemeanor is NOT a felon.