لم أفهم سبب هذا القرار، ثم فهمت الفكرة بعد الاجتماع.

Because لم changes how the verb works.

• أفهم by itself means I understand / I am understanding
• لم أفهم means I did not understand

In other words, لم negates the imperfect verb and gives it past-time meaning.

Grammatically, لم also puts the verb into the jussive mood. In fully vowelled Arabic, you would see:

• أفهمُ = I understand
• لم أفهمْ = I did not understand

In normal unvowelled writing, both look like أفهم, so the meaning comes from لم.

They come from the same root, ف-ه-م, but they are different verb forms:

• أفهم = I understand / I understand (imperfect)
• فهمت = I understood (perfect)

So the sentence uses:

• لم أفهم = I did not understand
• ثم فهمت = then I understood

This is very common in Arabic: one clause uses لم + imperfect for a negative past event, and the next clause uses the regular perfect for a completed past event.

Arabic often does not need a separate word for I, because the verb itself already shows the subject.

Here:

• أفهم = the prefix أ- shows I in the imperfect
• فهمت = the ending -تُ shows I in the perfect

So Arabic does not need أنا here. You could add أنا for emphasis, but it is not necessary.

In Modern Standard Arabic, when a demonstrative like هذا directly modifies a noun, the noun is normally definite and takes ال.

So:

• هذا القرار = this decision

This is the standard MSA pattern.

For English speakers, it may feel strange because English says this decision without a separate the, but in Arabic the noun after هذا is usually marked with ال.

Because سبب هذا القرار is a construct phrase (an iḍāfa-type structure), literally:

• سبب = reason
• هذا القرار = this decision

Together: the reason for this decision or literally reason of this decision

In this kind of structure, the first noun often does not take ال. So:

• سبب هذا القرار = the reason for this decision

Even though سبب has no ال, the whole phrase is still understood as definite because هذا القرار is definite.

Arabic often expresses this idea by using a noun combination rather than a preposition.

So instead of something exactly like:

• the reason for this decision

Arabic naturally says:

• سبب هذا القرار
• literally: reason of this decision

This is a very common difference between English and Arabic. English often uses of or for, while Arabic often prefers a construct phrase.

ثم means then, but with a sense of sequence and usually some gap in time or development.

So:

• لم أفهم ... ثم فهمت ... = I did not understand ... then I understood ...

Why not use other connectors?

• و = just and, a neutral connection
• فـ = so / then, often suggesting a more immediate result
• ثم = then, often after some interval or later stage

Here ثم fits well because the speaker first did not understand, and only later understood.

Because it refers to a specific idea, not just any idea.

• الفكرة = the idea
• فكرة = an idea

In this sentence, the speaker is talking about a particular idea that became clear after the meeting, so الفكرة is the natural choice.

بعد الاجتماع means after the meeting.

Breakdown:

• بعد = after
• الاجتماع = the meeting

This phrase tells you when the understanding happened:

• ثم فهمت الفكرة بعد الاجتماع = Then I understood the idea after the meeting

In fully vowelled Arabic, the noun after بعد is in the genitive:

• بعدَ الاجتماعِ

So this whole phrase functions like a time expression.

Because they answer what was or was not understood.

• لم أفهم سبب هذا القرار
  = I did not understand what?
  سبب هذا القرار

• فهمت الفكرة
  = I understood what?
  الفكرة

So both are direct objects.

In fully vowelled Arabic, they would be accusative:

• سببَ
• الفكرةَ

In ordinary unvowelled text, you do not see those case endings.

A fully vowelled version is:

لَمْ أَفْهَمْ سَبَبَ هَذَا الْقَرَارِ، ثُمَّ فَهِمْتُ الْفِكْرَةَ بَعْدَ الِاجْتِمَاعِ.

A careful reading would be approximately:

lam afham sabab-a hādhā l-qarāri, thumma fahimtu l-fikrata baʿda l-ijtimāʿi

A few useful things to notice:

• لم makes أفهم jussive: أفهمْ
• سببَ is accusative as the object
• القرارِ is genitive inside the construct phrase
• الفكرةَ is accusative as the object
• الاجتماعِ is genitive after بعد

In everyday reading or pause pronunciation, many final short vowels are not pronounced clearly, but this is the full grammatical form.