После объяснения учителя всё стало чётче.

Because после always takes the genitive case.

The dictionary form is объяснение.
Its genitive singular form is объяснения.

So:

• объяснение = nominative
• после объяснения = after the explanation

This is a standard pattern in Russian: many prepositions require a specific case, and после requires the genitive.

Because учителя depends on объяснения.

The phrase объяснение учителя means something like:

• the teacher’s explanation
• the explanation by the teacher

So the structure is:

• после
  • genitive noun: объяснения
• then a dependent noun showing whose explanation: учителя

This is very common in Russian. English often uses ’s or of, while Russian often uses the genitive:

• книга студента = the student’s book
• совет друга = a friend’s advice
• объяснение учителя = the teacher’s explanation

In this sentence, it most naturally means the teacher’s explanation.

Grammatically, Russian genitive after a noun can sometimes be ambiguous, especially with nouns formed from verbs. But in normal context, объяснение учителя is understood as an explanation given by the teacher, not an explanation about the teacher.

If someone wanted to make about the teacher clearer, they would usually phrase it differently.

Because всё means everything / it all, while все usually means everyone or all people/things in the plural.

Compare:

• всё стало лучше = everything became better
• все стали лучше = everyone became better

In your sentence, the subject is всё, which is grammatically neuter singular, so the verb is singular too.

Because the subject всё is grammatically neuter singular, and past tense verbs in Russian agree with the subject in gender and number.

So:

• он стал = he became
• она стала = she became
• оно стало = it became
• они стали = they became

Since всё behaves like a neuter singular subject, you get стало.

Because Russian often uses стать + comparative to mean become more ...

So:

• стало чётче = became clearer
• стало лучше = became better
• стало труднее = became harder

Here чётче is the comparative form, meaning clearer / more clearly depending on context. After стало, this comparative form is very natural.

You could also build a phrase with an adjective, but стало чётче is shorter and very idiomatic.

Because Russian comparatives do not always need an explicit than phrase.

In English, you often say clearer than before. In Russian, if the comparison is obvious from context, you can simply say:

• стало чётче
• стало лучше
• стало проще

The implied meaning is usually than before or than it was earlier.

If you want to say it explicitly, you can add something like:

• чем раньше
• чем до этого

But it is not necessary here.

It is best understood here as a comparative predicative form.

For learners, the simplest way to think about it is:

• чёткий = clear, distinct
• чётко = clearly
• чётче = clearer / more clearly

After verbs like стать, Russian often uses this comparative form in a way that does not map neatly onto just one English category. In practice, you should learn the whole pattern:

• стало чётче
• стало легче
• стало понятнее

These are very common and natural.

Yes, absolutely.

Russian word order is flexible. Both versions are correct:

• После объяснения учителя всё стало чётче.
• Всё стало чётче после объяснения учителя.

The difference is mainly emphasis:

• После объяснения учителя ... puts the time/context first
• Всё стало чётче ... puts the result first

The original sentence sounds natural and slightly foregrounds after the teacher’s explanation as the setup.

Yes. A very natural alternative would be:

• После того как учитель объяснил, всё стало чётче.

This uses a full clause: after the teacher explained.

The version with объяснения is more compact and slightly more noun-based in style, while the clause version is more explicit. Both are normal Russian.

No. It is a good, natural choice, but Russian could also use other comparatives depending on nuance, for example:

• яснее = clearer in the sense of easier to understand
• понятнее = more understandable
• чётче = clearer, more distinct, more sharply defined

So чётче suggests that things became more distinct or more clearly formed in the learner’s mind. In context, it works very well.