What's the difference between international and domestically flight ?

domestic flights stay within the country

An international flight is one that goes from one country to another. You need a passport for international flights.

A domestic flight is one that flies between two destinations in the same country. You do not need a passport for domestic flights.

International - flying from one country to another. You leave your country.
Domestic - flying within a country. You do NOT leave your country.

International - flying between two or more countries (eg. New York, USA to London, UK)
Domestic - flying within the same country (eg. New York, USA to San Fransisco, USA)

In general, security and check-in procedures are faster on domestic flights; and you only need photo ID instead of a passport.

For the US, on domestic flights, you only need a driver's license to show as ID. When you leave the destination airport, you do not have to go through immigration or customs. For an international flight, when you land you have to go through immigration (need a passport and possibly a visa in your passport) and you will go through customs.