What does the FIDE do besides the organize the international tournament? Or does the FIDE specialize in the tournament?
(I am not an expert so the following list will be incomplete.)
- calculate Ratings
- issue Titles (CM/WCM, FM/WFM, IM/WIM, GM/WGM)
- defines the chess rules
- umbrella organization for national organizations
- issue "Medal of Merit Awardees"
- and overall try to promote-improve chess (like try to make chess part of the Olympic games)
FIDE (Fédération Internationale des Echecs) is the world governing body for chess in the same way that FIFA (Fédération Internationale de Football Association) is the world governing body for soccer. You'll notice that both titles are in French. That's because these organizations were started almost 100 years ago when French was the language of international diplomacy. Today the principle language of FIDE is English and the definitive versions of the rules and regulations are the English versions. Where there is a conflict between the English version and a translation then the English version is the correct version.
FIDE is an international federation, so its constituents are national federations, although "national" is stretched a bit so that, for instance, the UK is represented by separate English, Scottish and Welsh "national" federations and conversely the Irish Chess Federation represents both the country of Ireland and the part of the UK called Northern Ireland. There are currently 188 member federations, but this number is almost constantly changing. These member national federations run chess in their regions and supply individuals to serve on the FIDE board and commissions. The chess competitions these federations run are for the most part run according to the rules and regulations laid down by FIDE.
There are also about 20 affiliated organizations. These include wider geographical organizations like the European Chess Union, special interest (language or race) organizations like the Francophone Chess Association and Arab Chess Federation and more loosely associated organizations like the International Computer Games Association, International Correspondence Chess Federation and the World Federation for Chess Composition.
There is a president and a board who form the "government" of FIDE and meet 4 times a year at quarterly presidential board meetings but the bulk of the work of administration is performed by the approximately 25 different commissions. These vary in importance from the Rules Commission, Anti-Cheating Commission, Events Commission to less critical ones like Commission for Chess in Museums and Commission of Chess Journalists, for example.
To give a complete answer to your question as to what FIDE does would involve describing the work of these ~25 commissions which would be very long indeed so I will make do with describing the functions of some of the more important commissions.
Rules Commission (https://ratings.fide.com/fide_directory.phtml?content=25)
This commission controls the FIDE Laws of Chess which define the layout of the pieces, how they move, how the game ends, how players should move, behave, handle the clock, record the moves, how the arbiter should behave, etc. The aim is to update these rules once every 4 years with improvements, updates and corrections. For instance, as digital clocks have replaced analogue clocks the rules have been updated to reflected changing technology. The latest version of the FIDE Laws of Chess (likely valid until summer 2017 when the next set of updated rules is expected to be authorized) is here https://www.fide.com/fide/handbook.html?id=171&view=article.
Anti-Cheating Commission (https://ratings.fide.com/fide_directory.phtml?content=9)
This is primarily concerned with preventing outside help for the chess player. Currently the emphasis is on detecting when this happens and steps to prevent it. More details here - https://www.fide.com/FIDE/handbook/Anti%20Cheating%20Guidelines.pdf.
Medical Commission (https://ratings.fide.com/fide_directory.phtml?content=22)
This commission investigates health related issues regarding chess. This includes on the one hand health benefits of chess and how healthy living can legitimately improve your chess and on the other the dark side of substances / drugs which can give illegal aid to the chess player. For more on all these topics see here - https://www.fide.com/fide/fide-anti-doping-regulations.html.
Qualifications Commission (https://ratings.fide.com/fide_directory.phtml?content=6)
This commission is responsible for regulating the FIDE Rating System and the FIDE titles for over-the-board competitions. For more on title regulations see here - https://www.fide.com/fide/handbook.html?id=10&view=category. For rating system rules see here - https://www.fide.com/fide/handbook.html?id=172&view=article.
Technical Commission (https://ratings.fide.com/fide_directory.phtml?content=24)
This is a high level commission which oversees technical aspects including control over other related commissions like the Rules Commission. As well as responsibility for the Laws of Chess (via Rules Commission) it also is in charge of tournament rules and regulations (https://www.fide.com/FIDE/handbook/Competition_Rules.pdf), Swiss Pairing Rules (https://www.fide.com/fide/handbook.html?id=18&view=category) and regulations for FIDE competitions.
Arbiters' Commission (https://ratings.fide.com/fide_directory.phtml?content=10)
This commission is in charge of setting the standards and training required for the different levels of FIDE arbiters (the chess equivalent of a referee in football). They appoint and govern FIDE arbiters. The FIDE regulations for the titles of arbiters is here - https://www.fide.com/fide/handbook.html?id=41&view=category.
Trainers' Commission (https://ratings.fide.com/fide_directory.phtml?content=30)
This commission is in charge of setting the standards, training and qualification of FIDE trainers. They appoint and govern FIDE trainers. The regulations for these titles are here - https://www.fide.com/fide/handbook.html?id=42&view=category.