There's no significance really. It's just a stereotypical lunch bag. I think most people use coolers these days, but back in the day you'd pack your sandwhich, chips, and drink in a brown paper bag to take to work.

Something like this.

https://images-na.ssl-images-amazon.com/images/I/41wfQvGOWFL...

It's just a generic term for a (usually low-cost) packed lunch from home, as opposed to going out and eating for lunch. It comes from how cheap lunches were packed in a brown paper back in the old days.

Brown bags are the classic container used to pack a lunch for a child attending school in the US. That practice dates back many generations, although I'm sure it's becoming rare in the last few decades.

Bag lunches can also be purchased at grocery stores and restaurants. So the brown implies that the lunch was purchased at home.

In 2018 a bag lunch from a grocery or restaurant is more likely to be brown than the one packed at home but the usage remains.

It's the cheapest disposable lunch carry you can purchase in the US that is tightly coupled to our cultural concept of frugal food expenses.

It's cheaper to make brown paper than white paper. Paper bags aren't bleached white because there's no functional need to do so.

It's an idiom for a cheap lunch made at home. At US stores all the very cheap lunch-sized disposable bags are brown for the most part.

in the context of a lunch container it conveys "nothing special", inexpensive, utilitarian, practical as opposed to fancy , expensive, extravagant "three martini" lunch

turn of phrase, just means making your own lunch.

edit: im wrong, it's an idiom.