I have never heard it in English either, and don't think it is a common term at all, but in Norwegian it is very common usage, where hvitevarer (white goods) is fridges, washing machines, dishwashers etc, and brunevarer (brown goods) are steroes, TVs etc.
If you go some decades back, almost all steroes and TVs were brown (typically wood or brown plastic), while dishwashers and fridges were nearly always painted white.
Brown goods because televisions and radios used to be in wooden cases, white goods because fridges and washing machines, etc. are typically painted white.
It's ordinary British English and as someone else pointed out common in other languages too. English: brown goods, white goods = Norwegian brunevarer, hvitevarer.
I'm not familiar with the "brown goods" term but I imagine it dates to when televisions with CRTs were typically housed in wood-paneled furniture while kitchen and washing appliances were typically white.
Never heard that kind of lingo before, it's weird ;)