Type theory isn't FP as much as logic--it applies everywhere. That said, totally agree that you're unlikely to have encountered it outside of an FP context in 2017.
Product and sum type are fundamental structures for construction of information. A product of two pieces of information is a piece of information equivalent to having both at once: it's sort of like "and". A sum of two pieces of information is a piece of information equivalent to having exactly one or the other and knowing which of the two you have: it's sort of like "xor".
Product and sum type are fundamental structures for construction of information. A product of two pieces of information is a piece of information equivalent to having both at once: it's sort of like "and". A sum of two pieces of information is a piece of information equivalent to having exactly one or the other and knowing which of the two you have: it's sort of like "xor".