If a Pokemon holding a lagging tail and uses a priority move, the priority will be priorited (hope you understodd what I meant there), so If you take a Pokemon with lagging tail, and uses Quick attack you will go first. But, If you have higher speed than opponent and uses a+1 priority move (for an example) , while your opponent uses a +1 priority move too, you will still go last because of the lagging tail.
Sorry If this just confused you Even more XD, but you can read the source for an better example.
Hope I helped :)