Learn Spanish (Spain): La reina escribía cartas en el palacio.

Escribía is the imperfect tense. We use it here because it describes an ongoing background action in the past (she was writing letters) or a repeated habit (she used to write letters). If we used the preterite escribió, it would mean she wrote a specific set of letters once, and the action was viewed as a single completed event.

The translation says "wrote", but can escribía also mean "was writing"?

Yes! The Spanish imperfect tense doesn't have just one English equivalent. Depending on the context of the story, escribía can be translated as "she wrote" (as a regular habit), "she used to write", or "she was writing".

How do I remember the imperfect endings for verbs like escribir?

Escribir is a regular -ir verb. To make the imperfect, you drop the -ir and add the ending for "she" (the queen), which is -ía. A helpful trick is that both -er and -ir verbs share the exact same endings in this tense, and every single one of those endings has a written accent on the í (like -ías, -íamos, and -ían).

Why is there no article before cartas? Shouldn't it be las cartas?