Learn Dutch: We lopen door de deur. - We walk through the door.

The lesson covers prepositions like naar (to) and in (in/into), but here we need door because it means through. You use it when passing from one side of something to the other, like going through a doorway.

I thought lopen meant to run. Why is it translated as walk here?

In Dutch, lopen is the general word for moving on foot and usually means to walk. It can sometimes mean to run in certain contexts, but if you want to clearly say to run, it is better to use the verb rennen.

How do I know to use de instead of het before deur?

Like most Dutch nouns, deur is a de-word. There is no simple rule for whether a word takes de or het, so it is best to memorize the article together with the noun when you first learn it.

Is the Dutch word door related to the English word door?

They look exactly the same but they are false friends! The Dutch word for the physical door is deur. The Dutch word door is a preposition meaning through. They also sound different: the Dutch door has a rounder, longer o sound.