The NHL Conference Finals mark the business end of the NHL Playoffs. The Western and Eastern Conference Finals are the 2 best-of-7 series that make up the third round of the Stanley Cup Playoffs and they're the last hurdle to jump to reach the Stanley Cup Finals.
Before the late 1960s, the league was a single division, but as the NHL expanded it has been split in two. Originally the sides were called the East Division and the West Division, then in the 1970s, they were renamed the Prince of Wales and Clarence Campbell Conferences, respectively (the names of which are still reflected in the trophies each conference champion lifts; the Prince of Wales Trophy for the Eastern Conference champion and the Clarence S. Campbell Bowl for the Western Conference champion). The first official Conference Finals were held in 1982, and since the early 1990s, the divisions have been known as conferences and are geographically split.
Don't expect to see the winners lift or even touch their respective trophy though – many players are superstitious about doing so as they consider the Stanley Cup the only one which should be hoisted!