In part Barbara is right and while the Omagh bombing was, without doubt, a major turning point in 'the troubles' in N.Ireland, the REAL turning point was 9/11.
It is no coincidence that N. Ireland's politicians were forced to the negotiating table by the events following 9/11 because, for the first time ever, Catholic Americans who had long supported the Republican movement by way of financial donations to 'the cause' saw for themselves what the real effects of supporting terrorism are. Consequently, they stopped handing over the money. In turn, this pushed Republicans to face the fact that they could not go on with thier campaigns without money and so, negotiations were essential if they were not to be left totally behind in the peace process.
So, if you are looking for a defining moment in modern Irish history, it is 9/11, not Omagh.