In the equipment regulations for FIFA competitions, section 18.2 states:
Those Member Associations that have won the FIFA World Cup may put a symbol on the playing shirt representing this accomplishment and the number of times won.
The form of symbol is not specified, although the accompanying illustrative example depicts a gold star.
For national team jerseys, each star displayed over the badge represents a men’s World Cup won by the country.
Brazil added three stars above their badge after winning their third World Cup in 1970. Italy did likewise in 1982. All world champions have since followed suit. Uruguay display four stars, regarding their triumphs in the 1924 and 1928 Olympics as equivalent to their later World Cup wins, as there was no World Cup at the time. In 2004, Denmark wore a star on their shirts specially for Euro 2004, to commemorate their victory in the competition in 1992.
- A win at the European Cup of Nations (Euro) is not supposed to be represented by a star.
- USA has 3 stars but those are part of the design of the badge. They do not mean anything in term of tournament victories. Stars have a significance only when they are embroidered above the badge.
- A women’s World Cup victory is also represented by a star, but it is usually worn on the sleeves. Women’s national jerseys also wear the stars won by the men above their badge (although the men do not display the women’s stars)
- At club level, stars have different meanings, depending of the country.
- In France, Italy and Portugal, 1 star means 10 league titles. Benfica players wear a jersey with 3 stars on top of the team's crest for its 36 "Primeira Liga" titles.
- Germany has two systems:
- The DFL (Bundesliga, 2. Bundesliga only):
- 1 star for 3 titles
- 2 stars for 5 titles
- 3 stars for 10 titles
- 4 stars for at least 20 titles
* Bayern Munich have 4 stars for its 27 Bundesliga wins (BM's 1932 title was won 31 years before Bundesliga started hence not counted).
- The DFB system (everything else, like Women's Bundesliga, 3. Liga, etc.):
- 1 Star for any club that won at least one championship in one of Germany's top domestic leagues (Bundesliga, DDR Oberliga, titles before 1963)
- optionally the number of titles can be imprinted on that star
- In Turkey, a club gets a star for each 5th championship. Hence, Galatasaray (21 wins) has 4 stars, Fenerbahçe (19) and Beşiktaş (15) have 3, Trabzonspor (6) has 1 star.
- In the US, 1 star means 1 MLS Cup.
- In some countries, the federation has no say whatsoever in the meaning of stars. Thus, the clubs can wear them for whatever reason they like. In Brazil, for example, some clubs would display stars for Second Division titles or state championship titles.
- Finally, winners of the UEFA Champions League do not wear stars above their badge: They wear, on the sleeve, a blue badge with the UCL trophy and the number of UCL titles won. However, they’re only authorized to display it when they play a UCL game.
For further reading look at Wikipedia article Star (football badge)