Or does he mean effectively unlimited, like a brain having 1000 YB[0] of storage and a human never coming close to experiencing that much information input in their lifetime?
[0] This number is made up and for illustrative purposes.
There are a few people with a condition called hyperthymesia, like Jill Price, and the condition generally has a profound negative impact on their lives.
Its not like there's an "erase" routine in our brains, it's just that the neural pathways start getting used more and more for other more important things. But there's still a readable trace of the old pathway there.
Sort of like the shortcut over the corner of the lawn where the grass can't grow because everyone goes there, but then when the new overpass is built people stop going there and new grass sort of grows over it but not completely because other people see the desire path and use it for other purposes every now and then so it never really disappears.