Художница должна была закончить открытку до вечера, чтобы успеть на поезд в порт.

The female painter had to finish the postcard by evening in order to catch the train to the port.

Breakdown of Художница должна была закончить открытку до вечера, чтобы успеть на поезд в порт.

• в: to
• вечер: the evening
• на: for
• поезд: the train

Questions & Answers about Художница должна была закончить открытку до вечера, чтобы успеть на поезд в порт.

Why is it художница and not художник?

Художница is the specifically feminine form of художник (artist, painter).

• художник – male artist or artist in general (can be generic).
• художница – explicitly female artist.

In modern Russian, the masculine form художник is often used generically, but if the speaker wants to make it clear that the artist is a woman, they say художница. The suffix -ница is a common way to form feminine nouns from masculine professions or roles (e.g. ученик → ученица, артист → артистка, писатель → писательница).

What exactly does должна была mean, and how is it different from just должна?

должна была is the past tense of the modal construction “must / was supposed to.”

• она должна сделать – “she must / has to do (it)” (present/future obligation).
• она должна была сделать – “she had to / was supposed to do (it)” (obligation in the past).

So художница должна была закончить… = “The (female) artist had to / was supposed to finish…”.
The auxiliary verb была (past of быть, “to be”) puts the obligation in the past.

Why is закончить in the infinitive form?