At the time leading up to the 1529 Siege of Vienna, the Ottomans were seen as being on the brink of conquering all Europe. The Pope and Emperor levied special taxes; Martin Luther wrote that all Christians should study carefully the Book of Daniel in preparation for living under infidel rule, and carefully teach their children the catechism.

I don't know much about how specifically the Ottomans were defeated at Vienna, but their campaigns through the Balkans all suffered from their army having to march all the way out from Constantinople through hard terrain in a short campaigning season; those factors would definitely help explain their defeat.

Why would the Turks want to conquer all of Europe?

The Enemy at the Gate by Andrew Wheatcroft answers this question fairly well. It's complicated, but I'd place the defeat due to two men, namely King Jan III Sobieski of Poland and Prince Eugene of Savoy. The former united his people and made a daring attack over dangerous terrain while the latter was one of the greatest generals of all time by most accounts. While it's arguable that the Ottomans were already well in decline at this point, this was a powerful turning point that led to the reclamation of much territory and the breaking of what Wheatcroft would call the European fear of the Ottomans.