The title: First of all the title, Ирония Судьбы, means the irony - Ирония - of fate. Fate is судьба and because it is of fate, we use родительный падеж, so судьба becomes судьбы. The full title is actually Ирония Судьбы или с Лёгком Паром - с Лёгком Паром is an expression that more or less means 'have a nice bath'. It is something you say to someone who is either going to, or coming from the sauna - Баня.
It's traditionally a movie that is watched on New Year's eve and its about guy who is about to get married who gets drunk with his friends. So drunk that he flies to St Petersburg instead of one of his friends. Thanks to communism, at the time all apartments looked the same and all streets/buildings had the same names in every city so he basically goes to the right address in the wrong city and in this wrong apartment meets a woman. It's worth a watch - extremely funny at parts. Well worth a watch - if alone because everyone in the Russian speaking world knows it.