"The woman sees the skirts."
Translation:Die Frau sieht die Röcke.
a single skirt -> "Die Frau sieht den Rock."; women -> "Die Frauen sehen den Rock/die Röcke." The case with both plural forms "Die Frauen sehen die Röcke." might be considered ambiguous but since skirts are not capable of seeing, the subject of the sentence can only be "Die Frauen". Accusative object in first position is possible but I'd say that subject in first position is more common.
"The woman sees the man." "The man sees the woman." Subject and object look alike. You need a fixed word order to distinguish between them. "Die Frau sieht den Mann." "Die Frau sieht der Mann." "Die Frau" can be subject or object (as in the second sentence) but "der Mann" is clearly nominative and "den Mann" is clearly accusative. So you needn't rely on the word order too much to distinguish subject and object. That is why the word order is not as fixed as in English.