Removing the seeds from a cucumber reduces the amount of watery liquid you get in the finished soup or salad in favor of the pure flesh of the cucumber. It's not always necessary (and the seeds are good for you), but it's easy to do when you want a more refined dish.

Slice the cucumber in half lengthwise. Then scoop the seeds out with the tip of a spoon. If you press down hard enough, one or two passes with the spoon should get most of the seeds.