A felony is generally described as a criminal offense punishable by imprisonment of more than one year or death. At common law the original felonies were arson, burglary, homicide, larceny, mayhem, rape, and robbery.
A felony stands in contrast to a misdemeanor, which has less severe penalties. However, some modern criminal statutes no longer distinguish misdemeanors from felonies, and instead classify offenses according to degrees, or levels of seriousness.
Whether someone is charged and convicted of a misdemeanor versus a felony can have serious consequences on such things as what types of jobs one can get, whether someone can vote, whether the crime will remain on one's record (committing a misdemeanor when under the age of 18 doesn't usually remain on one's record, while a felony can), and a variety of other things.
Additionally, it's important to know that the same criminal offense can be classified differently and carry different penalties in different states.