Learn Danish: Kvinden kigger på nederdelen, men hun vælger den der er stribet. - The woman looks at the skirt, but she chooses the one that is striped.

In this sentence, den der translates to "the one that". The word den acts as a pronoun replacing nederdelen (the skirt), and der is the relative pronoun connecting it to the rest of the sentence. If you only used der, the sentence would mean "...but she chooses that is striped", completely missing the object she is choosing.

Why is it den der and not det der?

The pronoun must match the gender of the noun it replaces. Since it refers to nederdelen (from the common-gender noun en nederdel), you must use den. If she were choosing an apple (et æble), which is a neuter-gender word, you would use det der.

Could I use som instead of der in this sentence?

Yes, you could absolutely say den som er stribet. Both der and som can be used as the subject of a relative clause. In everyday spoken Danish, however, der is slightly more common when it acts as the subject, as it does here.

Why does the sentence use kigger på instead of ser?

Kigger på implies an active, intentional action, much like "looking at" or "examining" in English. This is the natural choice when someone is inspecting an item in a store. Ser generally translates to "sees" and is used more for passive sight or suddenly noticing something.