Čím víc se učím češtinu, tím víc jí rozumím.

It is the Czech way to say the more …, the more …, the less …, the less …, and similar patterns.

So:

• Čím víc se učím češtinu, tím víc jí rozumím. = The more I learn/study Czech, the more I understand it.

This pattern is very common in Czech:

• Čím dřív, tím líp. = The sooner, the better.
• Čím víc čteš, tím lépe píšeš. = The more you read, the better you write.

In this construction, čím …, tím … is basically a fixed pair.

A helpful way to think about it is:

• čím = by how much / the more
• tím = by that much / the more

So literally, the sentence feels like:

• By how much more I study Czech, by that much more I understand it.

You do not need to analyze this every time; it is best learned as a set pattern:

• čím víc …, tím víc …
• čím méně …, tím méně …
• čím déle …, tím hůř/lépe …

Because učit se means to learn or to study.

This is important, because without se, the verb usually means to teach.

Compare:

• Učím se češtinu. = I am learning/studying Czech.
• Učím češtinu. = I teach Czech.

So in your sentence, se is essential. It tells you the subject is learning, not teaching.

Because češtinu is the accusative form, and učit se takes a direct object in the accusative when you say what subject you are studying.

• dictionary form: čeština = Czech
• accusative: češtinu

So:

• učím se češtinu = I study/learn Czech

This is the same kind of thing as:

• mám knihu from kniha
• vidím ženu from žena

The noun changes because of its role in the sentence.

Because jí means it / to it / her, and here it refers back to čeština.

So instead of saying:

• Čím víc se učím češtinu, tím víc rozumím češtině.

the sentence uses a pronoun:

• Čím víc se učím češtinu, tím víc jí rozumím.

That sounds natural and avoids repeating the noun.

Notice, though, that if you repeated the noun, it would not be češtinu in the second clause. It would be češtině. That is because the verb rozumět requires a different case.

Because rozumět takes the dative, not the accusative.

• jí = dative form here
• ji = accusative form

So:

• rozumím jí = I understand it/her
• not rozumím ji

If you used the full noun instead of the pronoun, you would say:

• rozumím češtině

This is one of those verbs you simply need to memorize with its case:

• rozumět + dative

Because the two verbs require different cases.

In the first clause:

• učit se češtinu
• češtinu is accusative

In the second clause:

• rozumět češtině
• češtině is dative

So even though both refer to the same language, the form changes because the grammar changes.

This is very normal in Czech. English usually keeps the noun the same, but Czech often changes the ending depending on the verb.

Because short pronouns in Czech often go in the second position in the clause.

In the clause:

• tím víc jí rozumím

the opening unit tím víc acts as the first position, and then the short pronoun jí comes right after it.

That is why jí appears before the verb.

This word order is very natural in Czech. If you move the pronoun elsewhere, the sentence may sound marked, less natural, or more emphatic.

Because Czech often leaves out subject pronouns when they are already clear from the verb ending.

Both verbs here show 1st person singular:

• učím = I learn/study
• rozumím = I understand

So Czech does not need já.

You could add já for emphasis, but normally it is unnecessary:

• Čím víc se učím češtinu, tím víc jí rozumím. = neutral
• Čím víc se já učím češtinu, tím víc jí rozumím. = more emphatic/contrastive

Yes. Both mean more.

• víc is very common and natural in everyday Czech
• více is a bit more formal or literary

So both of these work:

• Čím víc se učím češtinu, tím víc jí rozumím.
• Čím více se učím češtinu, tím více jí rozumím.

For most learners, víc is the form you will hear a lot in normal speech.

Because Czech writes a comma between the two parts of this correlative construction:

• Čím …, tím …

So the comma separates the two linked clauses:

• Čím víc se učím češtinu, tím víc jí rozumím.

This is standard punctuation in Czech, just as English normally separates the more …, the more … clauses.