Without going too much into the technicalities, Field Order is related to interleaved video, which yours is. Roughly it means that a video image is broadcast in two parts, or in sets of alternating lines. So if it is Upper Field First, lines 1, 3, 5 etc are broadcast first, followed a microsecond later by lines 2, 4, 6 and so on. It all happens so fast that the human eye sees it as one image. If it is Lower Field First, then lines 2, 4, 6 etc are broadcast, followed by lines 1, 3, 5 and so on.
But if, say, your original video is Lower Field First, and you render it using Upper Field First, then the resulting video will not be quite right. It may appear a little jerky, and straight lines will look jagged. That is why you need to get this right.