I get the the electricity is coming from the top and working its way down, what I don't understand is why the sparks keep going inside the glass after the nail is removed. Is it acting like a temporary battery holding a small charge for a short time?
Yes, it is a battery like effect. That's actually kind of how it works. The acrylic is charged with a particle accelerator, like a battery, trapping the electrons in it.
But, the electrons "don't want to be" in the acrylic, so when the blue grounding strip pierces the edge, they rapidly escape all at once, burning the channels you see.
The channels are more conductive than the surrounding acrylic and any residual charge courses along them.
.
See the links I posted above for more.
The acrylic is charged up and then rapidly discharged as shown in the gif.
Article:
http://www.dailymail.co.uk/sciencetech/article-1232908/Captured-lightning-The-artist-traps-fossilised-bolts-electricity-inside-acrylic-blocks.html
The video that gif is from:
https://m.youtube.com/watch?v=SYraS3LwbIo
Another, at 2 million volts:
https://m.youtube.com/watch?v=h57xNxG_tSg
But, the electrons "don't want to be" in the acrylic, so when the blue grounding strip pierces the edge, they rapidly escape all at once, burning the channels you see.
The channels are more conductive than the surrounding acrylic and any residual charge courses along them.
.
See the links I posted above for more.