No, but it was explained pretty well.
What I gathered from the exposition is that while the Time Lords and Daleks were inside the Time Lock, the Doctor was not. Ergo, he possessed "the moment," some sort of window where he could come and go from the Time War as he pleased.
I would like to think that something like this happened: The feud between the Daleks and Time Lords began. The Time Lords, under President Romana, recalled every Time Lord to Gallifrey. Needing all of their kind, they eventually set about resurrecting long dead Time Lords, including the Master and maybe even those inside the Matrix.
This included Time Lords who had lived and died during the Dark Time, which is what polluted the Time Lord race and caused them to use their great powers in such an evil manner. Eventually, Romana lost control of the High Council and Rassilon was resurrected, under the belief that he would be the architect of Time Lord victory. However, Rassilon,obsessed with his own immortality, set about using the Time War to his own ends. The Time Lords became even more corrupt, and Time itself turned against them.
The Doctor and Romana escaped together, and set about finding the six segments of the Key To Time. They then time locked the war, trapping both Daleks and Time Lords in it forever. The Master had by then run away as well, and perhaps a handful of others. Romana left for ESpace with a few good Time Lords to ensure the race would survive, much like the Cult of Skaro went into the Void, and the Doctor used the moment the Key To Time gave him to detonate Gallifrey's sun inside the Time Lock while the Daleks hovered above Gallifrey,all the forces gathered together, and nearly died in the process, triggering his regeneration as he catapulted the TARDIS away and through the confines of the Time Lock by using the Key to Time. Unknown to the 8th Doctor, the events of The End of Time unfolded on Gallifrey w/in the confines of the Time Lock, which was nearly broken. As Gallifrey was destroyed, some of the good Time Lords, like the Woman in White ascended, while the others, like Rassilon died. The Master, having entered from outside, was sent somewhere else, but the energy renewed his regeneration cycle. The Key to Time was also dispersed at that point, breaking the Time Lock once it was no longer needed, which is what allowed the Dalek Emperor's damaged ship and the lone Dalek to hurtle back through time & space.