La que més m'agrada és la verda.

La que means something like the one that or the one which.

In this sentence, la is not just the before a normal noun. It is standing in for an omitted feminine noun, such as la samarreta or la camisa. So la que més m'agrada means the feminine one that I like the most.

This structure is very common in Catalan when the noun is understood from context:

• El que vull = the one / what I want
• La que prefereixo = the one I prefer

So here, La que més m'agrada is a noun phrase meaning the one I like most.

M'agrada means I like it or more literally it pleases me.

Catalan uses agradar in a way that works like Spanish gustar:

• M'agrada = it is pleasing to me
• M = to me
• agrada = pleases / is pleasing

So the thing being liked is the grammatical subject, not the person who likes it.

That is why Catalan does not say something equivalent to I like in the same structure English does. Instead, it says something closer to:

• The green one pleases me the most

The apostrophe shows elision.

The unstressed pronoun em becomes m' before a vowel sound:

• em agrada → m'agrada
• em interessa → m'interessa

This is very common in Catalan. It helps the sentence flow more naturally in speech.

So m'agrada is simply the shortened form of em agrada.

Més means more or, in this context, most.

In La que més m'agrada, the idea is the one that I like the most.

Catalan often uses més with a relative clause like this to express a superlative idea:

• la que més m'agrada = the one I like most
• el que més vull = the one I want most
• la que més costa = the one that costs the most

So més adds the idea of most.

The accent in més is a written accent mark that distinguishes it from mes.

• més = more / most
• mes = month or an old/literary word for but

So the accent is important because it changes the meaning of the word.

The accent distinguishes és from es.

• és = is
• es = a reflexive or clitic pronoun, like oneself / each other / to oneself, depending on context

So in this sentence, és is the verb to be in the third person singular:

• és la verda = is the green one

The accent helps avoid confusion.

Because verda is being used as a noun-like expression: the green one.

Catalan often uses an article + adjective when the noun is omitted but understood:

• la verda = the green one
• el blau = the blue one
• les grans = the big ones

If you said only verda, it would normally sound incomplete here, because Catalan wants the article when the adjective stands in for a noun.

The noun is not stated, but it is understood from context.

For example, it could stand for:

• la samarreta verda = the green T-shirt
• la poma verda = the green apple
• la cadira verda = the green chair

Because the sentence uses la and verda, we know the missing noun is:

• feminine
• singular

So even if the noun is not spoken, the grammar still tells you what kind of noun it must be.

Because it agrees with the omitted noun represented by la.

In Catalan, adjectives usually agree in gender and number with the noun they describe:

• verd = masculine singular
• verda = feminine singular
• verds = masculine plural
• verdes = feminine plural

Since the sentence has la verda, the implied noun must be feminine singular.

Yes. That is also correct.

Both sentences are natural, but they focus on slightly different things:

• La que més m'agrada és la verda.
  This starts with the one I like most, then identifies it as the green one.

• La verda és la que més m'agrada.
  This starts with the green one, then says that it is the one I like most.

So the difference is mainly one of emphasis and information structure, not basic meaning.

Yes, in many contexts you can hear both, but La que més m'agrada is the more standard and natural order in this kind of relative clause.

Catalan often places més before the verb phrase when it modifies the degree of liking:

• la que més m'agrada

Putting més later, as in la que m'agrada més, may sound more conversational in some varieties, but the original version is a very solid model for learners.

The subject of és is the whole phrase La que més m'agrada.

So the structure is:

• La que més m'agrada = subject
• és = verb
• la verda = predicate/complement

In other words:

• The one I like most = subject
• is = verb
• the green one = complement

The articles and adjective would change to match the gender and number.

Examples:

• El que més m'agrada és el verd. = The one I like most is the green one.
  masculine singular

• Les que més m'agraden són les verdes. = The ones I like most are the green ones.
  feminine plural

• Els que més m'agraden són els verds. = The ones I like most are the green ones.
  masculine plural

Notice that agrada / agraden also changes depending on whether the thing liked is singular or plural.