La meva mare prefereix fregir el peix, però jo prefereixo bullir les patates.

In Catalan, a possessive adjective normally comes with a definite article: el meu, la meva, els nostres, and so on. So la meva mare is the standard pattern.

English says my mother with no article, but Catalan usually does not work that way.

No. Meva agrees with the thing possessed, not with the person who owns it.

Here, mare is feminine singular, so you get la meva mare.
If the noun were masculine singular, you would say el meu pare.

So a man and a woman would both say la meva mare.

They are two different present-tense forms of preferir:

• prefereix = he/she prefers
• prefereixo = I prefer

Catalan changes the verb ending depending on the subject. In the present tense, preferir goes like this:

• jo prefereixo
• tu prefereixes
• ell/ella prefereix
• nosaltres preferim
• vosaltres preferiu
• ells/elles prefereixen

So La meva mare prefereix... and jo prefereixo... are exactly what you would expect.

After preferir, if another verb follows, that second verb normally stays in the infinitive:

• prefereix fregir
• prefereixo bullir

This is like English prefer to fry / prefer to boil, except Catalan does not need a separate word like to here.

So:

• prefereixo bullir = literally I prefer boil, but naturally I prefer to boil

Yes, prefereixo already tells you the subject is I, so jo is not required.

It is included here for contrast: my mother prefers..., but I prefer...

Catalan often leaves subject pronouns out, but speakers add them when they want emphasis, contrast, or clarity. In this sentence, jo makes the contrast stronger after però.

Catalan uses definite articles more often than English does. With food items and direct objects, el, la, els, les are very common.

So fregir el peix and bullir les patates sound natural in Catalan, even where English might simply say fry fish or boil potatoes.

The articles also agree with the nouns:

• el peix = masculine singular
• les patates = feminine plural

Però means but. It links two contrasting ideas:

• La meva mare prefereix...
• però jo prefereixo...

The accent on ò shows where the stress goes and also indicates the vowel quality. In standard pronunciation, ò is an open o sound.

The comma before però is also normal, just like a comma before but in English when it joins two full clauses.

A few sounds here are especially useful:

• ll in bullir is traditionally a palatal sound, roughly like ly for an English speaker.
• x in peix and at the end of prefereix sounds like English sh.

Very rough English-style approximations:

• bullir ≈ boo-lyir
• peix ≈ paysh
• prefereix ≈ preh-feh-RAYSH or preh-feh-REHSH, depending on accent

These are only approximations, but they are enough to help you recognize the sounds.

This is the normal Catalan order:

subject + verb + infinitive + object

So:

• La meva mare = subject
• prefereix = conjugated verb
• fregir = infinitive
• el peix = object

Catalan word order is somewhat flexible, but this version is the most neutral and natural for a learner to use.