Learn German: Während der Kellner die Suppe serviert, spülen wir die Teller. - While the waiter serves the soup, we wash the plates.

The word während (while) is a subordinating conjunction here. That means it kicks the conjugated verb (serviert) to the end of its clause. This is the standard rule for all subordinate clauses in German, just like with weil or dass.

Why does the second part say spülen wir instead of wir spülen?

In German, the conjugated verb of a main sentence must be in the second position. Here, the entire während clause acts as the first position block. So, the verb spülen must come immediately after the comma to take the second position, pushing the subject wir after it.

I have seen während used with the genitive case before. Why isn't der Kellner in the genitive here?

Während can be used in two ways: as a preposition meaning during, which takes the genitive case, and as a subordinating conjunction meaning while, which connects two clauses. In this sentence, it is a conjunction introducing a new action, so der Kellner is simply the subject of that action in the nominative case.

Why use spülen for washing the plates instead of waschen?