That seems to be another American saying "brown bags" where we say lunch box or sandwich box which can be anyting from a clear plastic bag to a plastic Tupperware type box. We do not really use brown bags though I believe some take-away shops do put the food in them.
Years ago, "blue collar" workers took lunch boxes with them - so did most school kids.
White or pink collar workers didn't want to be grouped with those, so they took their lunch in paper bags.
Now we use the phrase "brown bag" when we mean "take your lunch", no matter what it is carried in.
It's a status thing, although probably few remember that.