Dissolving parliament is when you call another election, so that each member of parliament must be elected again by the people. This happened with Gough Whitlam in the 60s. What happened there is that Labor had the majority in both the House of Reps and the Senate, until a Senator died. When a Senator died he is replaced by the Premier of the state he was from (so, for example, if a Victorian Senator died, Ted Bailleu would just pick a replacement for him, no election needed). The problem there was that the state he was from (I can't remember which) had a Liberal majority, so the Liberal Premier picked his replacement, but he picked a man who was technically a member of the Labor party, but vowed to vote with the Liberal party. What then happened was that the now liberal majority in the lower house started blocking the bills introduced in the upper house by Labor. These included supply bills (bills to do with the money of the parliament). When supply bills are blocked, it is deemed that parliament are ineffective, because they can't get anything done, or even supply money to the country. So the Governer-general John Kerr dismissed the Whitlam government, saying they were ineffective and couldn't do the role of government. He dissolved the parliament, and called for another election (to get a real majority and fix the problem).
This is the best example to use when talking about the power of the crown, because they have the power to entirely change who is ruling the country. Whilst they don't do it often, they have the power and will use it when they deem it necessary.
I hope that helped, sorry if it just confused you more xD