To structure a base means using a special tool with ridged rolls to mark the base with a pattern for a quicker water wicking under the skis. In competition, the structure is as important as the waxing because it also allows to get the layer of water flowing under the skis.
To compare, the grooved tires of a car evacuate the rain way better than the slick tires, it also increases the control you have on the car. With the ski it is the same thing, the acceleration linked to the structure is extremely important, when you try two skis with different structures under each foot, you will quickly notice that one of the two feels like it sticks more to the snow which is not good.
Of course, this kind of tests is for experts or professionals, but to hand-structure a ski is not complicated and it can change the race. Especially on the long distance, the difference between the two structures can represent several minutes in the end.