Lottery miners are devices that can only win a block reward very seldomly because the hash rate the device is capable of (guesses per unit of time) is very small compared to total amount of hash rate trying to guess the correct hash (and subsequent difficulty). 

But sometimes due to chance the tiny amount of hash rate “miner” can manage to guess the right hash vs all the behemoths and win the block reward. So it’s in essence a lottery. 

If lottery hash hardware gets more capable, simpler and cheaper (as tech tends to do) then I could see millions of plebs plugging them in to both decentralize hash rate globally and to play the ultimate pleb lotto.