Mentre l'àvia preparava el sopar, l'avi descansava al sofà amb una manta.

Because Catalan often shortens the definite articles el and la before a vowel sound.

• la àvia → l'àvia
• el avi → l'avi

This is called elision. It works a bit like how English contracts I am to I'm, though here it affects the article.

Catalan often uses the definite article before family members when talking about them in a general, familiar way.

So:

• l'àvia = grandma / the grandmother
• l'avi = grandpa / the grandfather

In English, we often drop the article in this kind of sentence, but in Catalan the article is very natural.

They are in the imperfect tense.

• preparava = was preparing / used to prepare
• descansava = was resting / used to rest

In this sentence, the imperfect shows an action in progress in the past. Both actions form the background of the scene:

• Mentre l'àvia preparava el sopar...
• l'avi descansava...

A native English speaker can often think of this as was + -ing.

Mentre means while.

It introduces an action happening at the same time as another action:

• Mentre l'àvia preparava el sopar, l'avi descansava...
• While grandmother was preparing dinner, grandfather was resting...

It is a very common way to connect two simultaneous actions.

• mentre = while
• quan = when

Use mentre when two actions happen at the same time over a period:

• Mentre cuinava, escoltava música.
• While she was cooking, she was listening to music.

Use quan more for a moment or event:

• Quan va arribar, vam sopar.
• When he arrived, we had dinner.

In your sentence, mentre is right because both actions are ongoing at the same time.

El sopar means dinner or supper.

The noun is sopar, and with the article:

• el sopar = the dinner / dinner

Be careful: sopar can also be a verb meaning to have dinner.

So:

• el sopar = the meal
• sopar = to eat dinner

Here it is clearly the noun because it comes after the article el.

Al is the contraction of a + el.

• a el sofà → al sofà

So:

• al sofà = on the sofa or on the couch

This contraction is required in normal Catalan.

Compare:

• Va al mercat. = He goes to the market.
• Seu al sofà. = He sits on the sofa.

Catalan usually uses an article here: una manta = a blanket.

So:

• amb una manta = with a blanket

This suggests he has a blanket with him or over him. In English, we might say with a blanket, under a blanket, or wrapped in a blanket, depending on context. Catalan amb is broad enough to cover that general idea.

In this sentence, it most naturally means was resting.

Because it is in the imperfect tense, it describes an ongoing past action, not a finished one.

So:

• descansava = was resting
• not usually rested in this context

English simple past and progressive do not always match Catalan perfectly, but here was resting is the best fit.

They are the feminine and masculine forms:

• àvia = grandmother
• avi = grandfather

So in the sentence:

• l'àvia = the grandmother / grandma
• l'avi = the grandfather / grandpa

This is a common masculine-feminine pair in Catalan nouns referring to people.

The accent in àvia shows both stress and vowel quality.

• àvia is stressed on the first syllable: À-vi-a
• The à tells you it is an open a sound and marks the stressed syllable

Written accents in Catalan are important because they help with pronunciation and sometimes distinguish words.

It has two main parts:

1. Mentre l'àvia preparava el sopar

   • Mentre = while
   • l'àvia = grandmother
   • preparava = was preparing
   • el sopar = dinner

2. l'avi descansava al sofà amb una manta

   • l'avi = grandfather
   • descansava = was resting
   • al sofà = on the sofa
   • amb una manta = with a blanket

So the pattern is:

While + ongoing action 1, ongoing action 2.

That is why the sentence feels very natural and scene-setting in Catalan.