boxes are boxes Filipino
travellers use to transport items on airplane
trips to and/or from the Philippines
While some travellers actually use boxes explicitly made for this purpose (they are even labeled as "balikbayan boxes"), many others use any other corrugated cardboard box. Volumes range from 1 cubic foot (for carry-ons) to the maximum allowed by the airlines, usually around 8 cubic feet. The weight varies up to the maximum as well, usually from 60 to 80 pounds.
The boxes are sealed and reinforced with packaging tape. Some people further reinforce the boxes with twine or string. The string can double as handles, although I have seen some people make handles in other ways. Since corrugated boxes all look the same, personal identification is branded in large, bold letters on the side, and some people put other marks as well (such as brightly coloured paint). This minimizes mistakes at the luggage carousel.
These boxes are used instead of luggage since they have more volume and are well-suited to contain various gifts, items, and pasalubongs. The traveller essentially imports items for family and friends. Most airlines allow up to two boxes in check-in, already absorbed into the cost of the ticket, so to many, the hassle of lugging the boxes beats the price and risk of shipping them.
A friend of mine once worked as a luggage handler at Newark International Airport, and he said he could tell if the plane was headed to or coming from the Philippines simply by handling the boxes. It is certainly a testament to Filipino culture, one from which some jokes stem from, but is a practical solution nonetheless. I have seen non-Filipino travellers starting to adopt the boxes, but for me they will always be balikbayan boxes.