First, a few definitions:
Thundereggs were formed in a rare glassy, highly viscous, rhyolite lava flow. This silica rich lava is called perlite and the primary mineral within the glassy perlite that comes together to form the round nodules, is called cristobalite. Cristobalite is similar to quartz, just a little softer. Another mineral called cryptoperthite is around in small quantities to fill in the spaces of the cristobalite crystal structure.
This mineral formed sperulite is full of volatiles (gas) that create a cavity as the flow cools and the gas escapes. The cavities are usually filled with minerals (mostly quartz or opal) leached from the host rhyolite in a slow, banding inducing method.
* This explanation is based on the concepts outlined in the book by the Geode Kid. Thank you Robert... I hope I got it right.