До полудня мы успели пройти два квартала и купить кофе.

До полудня means before noon or by noon in this sentence.

• до = until / up to / before
• полудня = noon in the form required after до

So the phrase sets a time limit: all of this happened before noon.

Depending on context, English might translate it as:

• Before noon, we managed...
• By noon, we had managed...

Both capture the idea reasonably well.

Because the preposition до requires the genitive case.

The dictionary form is полдень (noon), but after до it changes to полудня.

So:

• полдень = nominative
• до полудня = genitive after до

This is a very common pattern in Russian:

• до утра = until morning
• до вечера = until evening
• до дома = as far as the house / up to the house