A brand name for fairly soft, rather rough (in fact actually hairy) printing paper suitable for use with mimeographs and hence used sometimes for printing fanzines. It absorbed ink and hence reduced the need for slipsheeting, while still not suffering badly from showthrough. Not everybody liked how it felt to handle, though.
There was at least one other brand of somewhat similar paper, called Fibertone (made by a Minnesota paper mill, which may explain why fans ran into it more commonly in Minneapolis.)
Twilltone is now a lost technology and is a minor object of worship among the most hard-core mimeographers in fandom.
See also: My Life As a Faned