Figuratively speaking, to "turn the page" on something is to leave an event or series of events behind and continue on with life.
If one phase of a series of events can be likened to a page, to turn the page is to make that series of events into history. This seeks to express that there has been some kind of fundamental shift, an irreversible change that marks a new phase in life.
Example: On August 31, 2010, U.S. President Barack Obama declared an end to U.S. combat operations in Iraq in accordance with its Status of Forces Agreement with Iraq. In doing so, Obama's staff told the news media that he would absolutely not use the words Mission Accomplished in regards to Iraq. (A careful reader of my post on "Mission Accomplished" will note that technically, President Bush did not speak the words either. They were simply on a highly visible banner.)
Instead, President Obama said, "It is time to turn the page." This wording was intended to convey that a new phase had begun in Iraq, a phase intended to be different from the old one, and better than the old one. However, even though the words are different, the meaning of "time to turn the page" and "Mission Accomplished" is extremely close, to the point of being virtually identical. It is obviously the hope of the Obama administration that listeners will view Obama's statement as having the "proper" meaning without being "tainted" by a phrase using different words, with an identical meaning, used years earlier in a way that was thought, in hindsight, to be unwise and improper.
In other words, this time, we really mean it.