Когда мой брат услышал эту шутку, он засмеялся.

Когда introduces a time clause and means when here.

So the sentence has two parts:

• Когда мой брат услышал эту шутку = When my brother heard this joke
• он засмеялся = he laughed / started laughing

This is a very common Russian pattern: когда + clause, then the main action.

Because Когда мой брат услышал эту шутку is a subordinate clause. In Russian, subordinate clauses are normally separated by commas.

So:

• Когда мой брат услышал эту шутку, он засмеялся.

If you reverse the order, you still use a comma:

• Он засмеялся, когда мой брат услышал эту шутку.

Because шутка is the direct object of услышал.

The base form is:

• эта шутка = this joke (nominative)

But after a transitive verb like услышать = to hear, the direct object goes in the accusative:

• эту шутку = accusative singular

Both words change because the adjective/demonstrative and noun must agree:

• эта → эту
• шутка → шутку

This is an aspect question.

• слышать = imperfective, to hear in a general/ongoing/repeated sense
• услышать = perfective, to hear as a completed event, to catch/hear something

Here the brother heard the joke at one specific moment, so Russian uses the perfective услышал.

Compare:

• Он слышал эту шутку много раз. = He had heard this joke many times.
• Он услышал эту шутку и засмеялся. = He heard this joke and laughed.

Literally, засмеялся means started laughing or burst out laughing.

In many English translations, it is simply rendered as laughed, because that sounds more natural in context. But the Russian verb highlights the beginning of the laughter.

So this sentence has a slight sense of:

• When my brother heard this joke, he started laughing.

They are both important parts of the verb.

• смеяться = to laugh
• за-смеяться = to begin laughing

The prefix за- often gives the meaning to start doing something.

The ending -ся is a reflexive marker, but with смеяться / засмеяться it is just part of the normal verb form. You do not translate it as himself here. So:

• смеяться = to laugh
• засмеяться = to start laughing

Because they are past-tense masculine singular forms.

In Russian past tense, verbs agree with gender and number:

• masculine: -л
• feminine: -ла
• neuter: -ло
• plural: -ли

Since брат and он are masculine singular, you get:

• услышал
• засмеялся

If the subject were feminine:

• Когда моя сестра услышала эту шутку, она засмеялась.

Yes, Russian often omits subject pronouns when the meaning is clear.

So this would also be natural:

• Когда мой брат услышал эту шутку, засмеялся.

But many speakers would prefer to keep он here for clarity and smoothness, especially because the sentence has two clauses. Including он makes the structure very clear:

• first clause: my brother heard the joke
• second clause: he laughed

So он is not strictly necessary, but it is perfectly normal.

Because Russian has no articles.

English needs words like a and the, but Russian usually expresses that idea through context, word order, or words like этот / эта / это = this.

Here эту already makes the noun specific:

• эту шутку = this joke

If it were just шутку, the meaning could be something like a joke or the joke, depending on context.

Yes. Russian word order is flexible, and changing it usually changes emphasis rather than the basic meaning.

The original sentence is neutral and natural:

• Когда мой брат услышал эту шутку, он засмеялся.

Other possible versions include:

• Мой брат засмеялся, когда услышал эту шутку.
• Когда эту шутку услышал мой брат, он засмеялся.

These versions shift focus a little. For example, putting эту шутку earlier may emphasize this joke in contrast with something else.

Yes. If it is obvious that the same person is doing both actions, Russian often avoids repeating the subject.

So you can say:

• Когда мой брат услышал эту шутку, засмеялся.
• Мой брат засмеялся, когда услышал эту шутку.

In the second version, it is especially natural to omit он, because мой брат has just been stated as the subject of the main clause.

Still, the original version with он is completely correct and sounds clear and natural.