Here's how it's explained in the Jewish Chronicle:
[Blair's] vision for Britain's place in the world, side by side with the United States in the promotion of democracy and liberty, was coupled with a second vision. He was convinced that the Middle East could be transformed - indeed was ripe for change - and that the sting of radical Islam could be drawn by bringing about political reform, including regime change in Iraq, whilst resolving the Israeli-Palestinian conflict.
In his July 2002 memo to President Bush, Mr Blair declared: "Getting rid of Saddam is the right thing to do", not only because "he is a potential threat", but because "His departure would free up the region." And in another private memo shortly after the invasion he began: "Our fundamental goal is to spread the values of freedom, democracy, tolerance and the rule of law, but we need a broad based agenda capable of unifying the world to get it. That's why, though Iraq's WMD is the immediate justification for action, ridding Iraq of Saddam is the real prize."
So where did the Israeli-Palestinian conflict come into this?
It was not that Mr Blair believed Israel's actions caused Al Qaeda's anti-Western Jihad, as some of the Labour left did, but because he believed it was the lever which steered Arab and wider Muslim opinion. It was, he said in the July 2002 memo, "essential" because, for the Arabs, "this is the very soul of their attitudes."
Resolving it, or at least attempting to, would undermine Al Qaeda's propaganda, cool Arab opinion towards the West, and make it easier for Arab states to get on board. It would also help manage the left of his own party, for whom the Palestinian issue had an outsized significance.
Tony Blair bent President Bush's ear on "MEPP" (Middle East Peace Process) so often that he would apologise in his memos for being a "bore" on the subject.
Indeed he is still hammering away at Israeli-Palestinian peace now, running a self-starter peace mission in Jerusalem, even after stepping aside as Quartet envoy...Clearly, Tony is the grip of an unhealthy obsession that cries out for intervention by a competent shrink.