Learn Hardcore Spanish (Spain): La profesora empezó a murmurar la respuesta mientras miraba el texto. - The teacher started to murmur the answer while looking at the text.

In Spanish, the definite article is often used where English would just say the teacher or sometimes even simply teacher in context. La profesora means the female teacher.

Also, profesora is specifically feminine. If the teacher were male, it would be el profesor.

Why does the sentence use profesora instead of maestra?

Both can mean teacher, but they are not always used in exactly the same way.

Profesora is very common for teachers in general, especially in secondary school, university, or formal contexts.
Maestra often refers more specifically to a primary-school teacher, though usage can vary.

So la profesora sounds natural here and may suggest a more general or formal teacher.

Why is it empezó a murmurar and not just murmuró?

Because empezar a + infinitive means to begin/start doing something.

So:

empezó a murmurar = she started to murmur / she began murmuring
murmuró = she murmured

The version with empezó a focuses on the beginning of the action, not just the action itself.