Okay, so I'm no expert on dryers or clothing, but I'll take a crack at simplifying as best i can
Electricity follows the path of least resistance. A conductor is something that allows electricity to flow freely. When a good conductor is present, electricity typically wants to jump on to it as it has very little resistance.
Now some dryers are good enough conductors that static isn't even an issue. Personally my dryer doesn't leave any static on my clothing, but my last one used to. I'd imagine it's because it's not as good of a conductor/grounding source. For example in my case, i could throw a load of 10 shirts in and maybe half of them would be left with leftover static. So the dryer did ground some of it, but it wasn't good enough to get all of it off of the shirts (my best guess is some shirts just weren't in contact with the dryer edge as much as others). In this case, the shirts need help to release their charges.
Cotton is a poor conductor. So once it builds up the static, the electricity doesn't move very easily.
If you were to throw in a known good conductor, such as a ball of foil, the shirts would be more prone to release their charges. The foil would act as a sort of catalyst to get the charges moving. Once the foil gets the charge, the only thing it wants to do is get grounded. So as soon as it's close enough to a grounding source it gets released.
Think about a group of 10 children and 1 parent (the children are the clothes and the parent is the foil). Now each child has $1(static charge) to spend at the store. Upon getting to the store, the children see the cashier is a scary looking guy (the dryer drum). Half the children get close enough to the cashier to see he's not so bad and proceed with their transaction (transferring the charge to the ground). The other half don't get near the cashier so are too afraid to proceed with their transaction. Upon seeing this, the parent takes the money from the children and completes the purchases for them (the foil taking the charge and grounding it).
Not the greatest analogy, but the best i can do.
TLDR: The foil picks up the charges from the clothing that couldn't get grounded and does it itself