Mi tía dice que las albóndigas con chorizo saben mejor al día siguiente.

Because the subject of the verb is las albóndigas con chorizo, which is plural. In Spanish, verbs must agree with the subject:

• la albóndiga ... sabe
• las albóndigas ... saben

So saben matches the plural noun albóndigas.

Yes, saber often means to know, but it also has another meaning: to taste / to have a flavor.

Examples:

• Sé la respuesta. = I know the answer.
• La sopa sabe bien. = The soup tastes good.

In this sentence, saben mejor means taste better, not know better.

Spanish uses articles more often than English. Here, las albóndigas refers to the meatballs in a general but definite way, as the topic being discussed.

Spanish often prefers the article where English might leave it out:

• Me gustan las manzanas. = I like apples.
• Las albóndigas saben mejor... = Meatballs taste better...

So las sounds natural in Spanish.

Because con chorizo describes the type or ingredient of the meatballs: meatballs with chorizo. It is a general ingredient phrase, not a specific piece of chorizo already identified.

Compare:

• albóndigas con chorizo = meatballs with chorizo
• albóndigas con el chorizo que compré ayer = meatballs with the chorizo I bought yesterday

So no article is needed here.

Literally, al día siguiente is something like on the following day or by the next day. In natural English, it is usually the next day.

al is a contraction of:

• a + el = al

So:

• al día siguiente = on the next day / the following day

This is a very common expression in Spanish.

In Spanish, many adjectives can come after the noun, and siguiente commonly does so in time expressions:

• el día siguiente = the following day
• la semana siguiente = the following week

You may sometimes see adjectives before nouns in Spanish, but with siguiente, the post-noun position is very standard here.

After verbs of saying, thinking, believing, etc., Spanish commonly uses que to introduce the next clause.

So:

• Mi tía dice que... = My aunt says that...

This is very normal:

• Creo que... = I think that...
• Pienso que... = I think that...
• Ella dice que... = She says that...

English often drops that, but Spanish usually keeps que.

Because mejor is the normal comparative form of bueno in many contexts, including taste.

• bueno = good
• mejor = better

So:

• saben bien = they taste good
• saben mejor = they taste better

Using más bueno is usually not the standard choice here.

Because mejor here is not acting like a regular adjective directly describing the noun. It is working with the verb saben to express taste better.

So:

• Las albóndigas saben mejor. = The meatballs taste better.

But if mejor were clearly describing plural nouns as an adjective, you might see plural agreement in other structures. In this sentence, saben mejor is a fixed and very natural verbal expression.

Mi means my. It does not change for masculine or feminine singular nouns:

• mi tío = my uncle
• mi tía = my aunt

For plural nouns, it is still usually mis:

• mis tíos
• mis tías

So mi stays the same for singular masculine and feminine nouns.

The accent mark shows where the stress goes and helps separate vowel sounds.

• tía is pronounced with stress on the í
• It is pronounced as two syllables: tí-a

Without the accent, the pronunciation rules would suggest something different. The accent helps show the correct spoken form.

The same applies to día and albóndigas, where the written accent marks indicate the correct stress.

Not exactly. Since this is Spanish from Spain, chorizo usually refers to the Spanish sausage, which is typically cured or semi-cured and seasoned with paprika. English speakers may know chorizo from different cuisines, but in Spain it normally refers to the Spanish version.

So in this sentence, a learner should think of Spanish chorizo.

Yes, but the meaning shifts slightly.

• saben mejor focuses on taste
• están mejor is broader and can mean are better overall

So:

• Las albóndigas con chorizo saben mejor al día siguiente = They taste better the next day.
• Las albóndigas con chorizo están mejor al día siguiente = They are better the next day.

In your sentence, saben mejor is more precise because it is specifically about flavor.