The word "toxin" has become a signal for pseudoscientific medicine, so I also furrowed my brow at that. But the original use of the word is much more clear in context. From the abstract which tokenadult kindly linked to:

Thus, the restorative function of sleep may be a consequence of the enhanced removal of potentially neurotoxic waste products that accumulate in the awake central nervous system.

Also, regarding the dangers of sleep deprivation, the first paragraph of the paper are relevant (http://www.sciencemag.org/content/342/6156/373.full):

Sleep deprivation reduces learning, impairs performance in cognitive tests, prolongs reaction time, and is a common cause of seizures (3, 4). In the most extreme case, continuous sleep deprivation kills rodents and flies within a period of days to weeks (5, 6). In humans, fatal familial or sporadic insomnia is a progressively worsening state of sleeplessness that leads to dementia and death within months or years (7).

Reference 7 is http://www.thelancet.com/journals/laneur/article/PIIS1474-44..., but I found the Wikipedia article more consumable for someone who is not up on medical research: http://en.wikipedia.org/wiki/Fatal_familial_insomnia