A medida que hablábamos del viaje, mi madre se fue animando.

A medida que means as or as/while, with the idea that one thing changes gradually at the same time as another.

So in this sentence, it shows that the more we talked about the trip, the more my mother became enthusiastic.

It is a very common structure for describing parallel development:

• A medida que estudiaba, entendía más.
  As I studied, I understood more.

You can think of it as stronger and more gradual than a simple cuando (when).

Here hablábamos is the imperfect tense of hablar.

The imperfect is used because the talking is presented as an ongoing background action. The sentence focuses on a process:

• A medida que hablábamos... = As we were talking...

If you used the preterite, it would sound more like a completed event, which does not fit as naturally with a medida que, because that expression usually highlights something unfolding over time.

So:

• hablábamos = we were talking / we used to talk
• here: we were talking

Both can be possible in Spanish, but they are not always equally natural.

• hablar de algo = to talk about something
• hablar sobre algo = to talk about something, often a bit more formal or more like a topic of discussion

In everyday Spanish, hablar del viaje is the most natural choice here.

Also, del is just the contraction of de + el:

• de el viaje → del viaje

So:

• hablábamos del viaje = we were talking about the trip

Se fue animando means she gradually became more animated / more cheerful / more enthusiastic.

This is a very useful pattern in Spanish:

• ir + gerundio

When used like this, it often shows gradual change over time.

So:

• se fue animando = she gradually cheered up / she slowly got more excited

It is not just she got excited in one instant. It suggests a progressive emotional change.

The verb here is animarse, not just animar.

• animar can mean to encourage someone
  
  • La animé. = I encouraged her.
• animarse means to become encouraged / to cheer up / to get enthusiastic

So mi madre se fue animando means your mother herself changed state.

That se is part of the pronominal verb animarse.

Not exactly.

• se animó = she cheered up / she got encouraged / she became enthusiastic
  This can sound more like a single completed change.
• se fue animando = she gradually cheered up / she was getting more and more enthusiastic
  This clearly emphasizes the process.

So the sentence uses se fue animando because it matches a medida que very well: both express something happening little by little.

Both forms can exist, but they are not exactly the same.

• irse + gerundio often emphasizes that something gradually develops and reaches a result
• ir + gerundio can also show gradual progress, but without the same nuance of change unfolding toward a new state

In se fue animando, the structure suggests that as the conversation continued, your mother progressively became more enthusiastic.

You may also see:

• se iba animando = she was gradually getting more enthusiastic

That version sounds a bit more descriptive and less bounded.
Se fue animando feels very natural here because it presents the emotional change as a process that happened during that conversation.

Animando is the gerund of animar.

In Spanish, the gerund often works like English -ing forms, but the uses are more limited. Here it is part of the verbal structure:

• irse + gerundio

So animando does not mean animating in a literal English sense here. Together with se fue, it means something like:

• she gradually became more animated / more encouraged

By itself, animar often means to encourage, but in this sentence the reflexive structure changes the meaning:

• animar a alguien = to encourage someone
• animarse = to cheer up / get encouraged / get enthusiastic

So mi madre se fue animando cannot mean my mother gradually encouraged without an object. It means your mother herself became more animated or enthusiastic.

Spanish often allows flexible word order, especially when the subject is already clear from the verb.

The sentence starts with the time/process clause:

• A medida que hablábamos del viaje...

Then it gives the main clause:

• mi madre se fue animando

This order is very natural because it sets the scene first and then tells you what happened.

You could also say:

• Mi madre se fue animando a medida que hablábamos del viaje.

That means the same thing. The original version simply puts more emphasis on the gradual context first.

Yes, sometimes.

Possible alternatives include:

• conforme
• según
• sometimes mientras

For example:

• Conforme hablábamos del viaje, mi madre se fue animando.

But a medida que is especially good when you want to stress gradual change. In this sentence, it is probably the best choice.

Although the exact meaning may already be given, learners often wonder about the tone.

This sentence has a gradual, natural, conversational feel. It suggests that at first the mother may not have been very excited, but as the conversation about the trip continued, she started to warm to the idea.

Natural English versions could be:

• As we talked about the trip, my mother gradually became more enthusiastic.
• The more we talked about the trip, the more my mother cheered up.
• As we were talking about the trip, my mother started getting more and more excited.

The best translation depends on context, especially what kind of animarse is meant: cheer up, warm to it, or get excited.