The Inter-Cities Fairs Cup, or just Fairs Cup for short, was Europe's first attempt at a secondary continental competition. Founded in 1955, same year as the UEFA Champions League, the Fairs Cup wasn't actually organized by any official soccer entity. Instead, it was organized by the Fairs Cup Committee which was led by certain FIFA executives.
At the time, it was common for cities in Europe to host trade fairs and for friendly soccer match to held to promote the event, hence the name of the tournament. In the beginning it wasn't taken too seriously, often cities would send a "national team" of players who played in different clubs from that city. The first champion for example was Barcelona XI, who played the final against London XI.
As the tournament evolved cities would choose a specific clubs to represent them, and eventually, in 1964, based on a league table criteria as well. Throughout the 60's the tournament continued to grow, with certain editions being compromised of up to 64 clubs. In 1971 UEFA took control, discontinued the tournament, and created the UEFA Cup (known today as the Europa League).
It is interesting to see the Fairs Cup editions one by one, you can clearly see the cup growing every year, and there are many clubs who get far that would be unimaginable today. The Spanish clubs dominated, Barcelona being the biggest champion with 3 titles, but Ferencvaros, Real Zaragoza, Dinamo Zagreb, and Leeds United won the cup, and Anderlecht and Ujpest reached the final as well.
Even though neither FIFA or UEFA consider the Inter-Cities Fairs Cup an official tournament, nor do the results of the tournament count for the clubs international record, the cup is still considered to be the predecessor of the Europa League. Today's second most important European club tournament originated from friendly matches to commemorate trade fairs.