A very long explanation would be needed. The shortened version is that it's a mechanism for resolving differences between the two Houses, the Senate and the House of Representatives, where the Senate has failed to pass legislation on two occasions that the House of Representatives has initiated. It's a mechanism by which those sorts of deadlocks and disagreements between the Houses can be resolved. They're resolved by means of a general election, and unusually it's a general election for the full composition of both Houses. Usually for our Senate, there's only a half-Senate election. At each election period, only half the Senate is re-elected, but with a double dissolution the full Senate is dissolved and there's an election for the full Senate. That's the difference between our two election patterns, and that's quite a novelty for you in Canada, where you don't have an elected upper house.
On May 17th, 2016. See this statement in context.