In the context of the laws of states of the United States, fornication is generally defined as (vaginal) sexual intercourse between two unmarried persons of opposite sex, and is a crime. However, most of those laws have been repealed or are not actually enforced nowadays.
In many Muslim countries, fornication, at least for the female partner, is a felony, and may be very severly punished. See Islamic Law.
The word is often used in a biblical context, where its meaning is open to intepretation. The etymology of the English word leads to the Latin word fornix, meaning "an archway" or "vault" (a reference to a location in Rome where prostitutes could be solicited). Scripture also uses the word to refer to a more generic failure to follow the word of God.
The origin of the word leads to a common usuage to specifically mean "whoredom" rather than general extra-marital sex.