It is the very first official screening of the film. The majority of the largest festivals require the screenings of submitted films to be World Premieres. If you show your film at some festival in April, you can forget about Cannes, because the movie just will not follow the regulations: the World Premiere has already taken place.
International Premiere is somewhat of a broader concept. On the one hand, it is the first screening outside the country of origin. On the other hand, it is a screening at an international festival. For example, let's say you have a film produced in Russia which is selected for Locarno, Moscow International Film Festival and major Russian National Festival "Kinotavr". If you send the movie to "Kinotavr", then the festival in Locarno will also show the movie. Seeing as the first case is a National Premiere and the second is an International one, requirements of both festivals will be met. However, screening your movie both at Locarno and at MIFF would not be possible because MIFF, in contrast to "Kinotavr", is an international festival, therefore a screening there is equivalent to an International Premiere even though it happens in the country of origin.
National premiere is, on the one hand, the screening of the film in the country of origin (a screening of a Russian movie at "Kinotavr" is equivalent to World and National Premieres, and the chance of an International Premiere still remains – at foreign festivals) and, on the other hand, it is the premiere in the specific country. For instance, if you screen the movie in France after a screening at "Kinotavr", then this screening will be an International and French Premiere at the same time.
It is obvious that the premiere requirements for a certain continent are usually set by the large and status festivals (for example, the rules for applying for Toronto festival specify that the films selected in its program should not have been previously screened in North America), and city premieres are often arranged at small festivals after the film appears at larger venues.
There is also the concept of a regional premiere. The festival in Abu Dhabi, for example, favors World and International Premieres, but strictly adheres only to the rule of Regional Premieres. If you have screened Russian film in Moscow and Cannes, there is still an opportunity to go to Abu Dhabi, as the region is defined by the festival as the "Persian Gulf" and screening will be treated as a Persian Gulf Region Premiere. Difinition of the region can we widen or shorten to any specific place, even to a concrete state/county or town.