عندما كنا نخرج من مكتب البريد، كانت أمي تحمل الطابع الآخر.

عندما means when. It introduces a time clause, so the part after it sets the time for the main action.

Here:

• عندما كنا نخرج من مكتب البريد = when we were going out of the post office / when we were leaving the post office

Then the main clause is:

• كانت أمي تحمل الطابع الآخر = my mother was carrying the other stamp

So عندما connects the two ideas as a time relationship.

Because كنا نخرج gives an ongoing past sense: we were going out / we were leaving.

• خرجنا = we went out / we left
  This sounds more like a completed event.
• كنا نخرج = we were going out / we used to go out
  This describes an action in progress or a repeated past action.

In this sentence, the most natural reading is an action in progress in the past: while we were in the process of leaving, something else was happening.

For the same reason: كان + imperfect verb often describes an action that was ongoing in the past.

So:

• كانت أمي تحمل = my mother was carrying
• حملت أمي = my mother carried

Using كانت helps show that both actions were happening at the same time in the past:

• we were leaving
• my mother was carrying

This is very common in Arabic narrative style.

Because the subject is أمي = my mother, which is feminine singular.

So the verb كان must agree with it:

• كان = masculine singular
• كانت = feminine singular

Since أمي is feminine, Arabic uses كانت.

The basic meaning of نخرج is we go out or we exit.

In context, من مكتب البريد makes it sound natural in English as:

• we were going out of the post office
• we were coming out of the post office
• we were leaving the post office

So the literal sense is go out, but idiomatic English often uses leave or come out of here.

مكتب البريد means post office.

Literally, it is something like:

• مكتب = office
• البريد = mail/post

Together, they form an iḍāfa construction, often called a noun phrase of possession or specification:

• مكتب البريد = the office of the mail = the post office

After the preposition من (from), the phrase becomes:

• من مكتب البريد = from the post office

أمي means my mother.

It is made of:

• أم = mother
• ـي = my

So this is a noun plus a possessive suffix:

• أمي = my mother

This is very common in Arabic:

• أبي = my father
• أخي = my brother
• أختي = my sister

In this context, الطابع most naturally means stamp, especially because the sentence mentions a post office.

So:

• الطابع = the stamp
• الآخر = the other

Together:

• الطابع الآخر = the other stamp

Outside this context, طابع can have other meanings too, such as character, nature, or imprint, but here stamp is clearly the intended meaning.

Because الآخر is describing a definite noun: الطابع = the stamp.

In Arabic, adjectives usually match the noun they describe in definiteness. So:

• طابع آخر = another stamp / a different stamp
• الطابع الآخر = the other stamp

That is why الآخر also takes الـ.

Yes. Here الآخر is functioning as an adjective describing الطابع.

Arabic adjectives normally come after the noun, unlike English. So the order is:

• الطابع الآخر
• literally: the stamp the-other
• natural English: the other stamp

This noun + adjective order is standard in Arabic.

Not always. It can mean a few related things depending on context, especially:

• was doing something
• used to do something
• sometimes a general past state or ongoing background action

So:

• كنا نخرج could mean we were leaving or, in another context, we used to go out
• كانت أمي تحمل most naturally means my mother was carrying

In this sentence, the context strongly suggests two actions happening at the same time in the past.

A careful fully vocalized reading would be:

عِنْدَمَا كُنَّا نَخْرُجُ مِنْ مَكْتَبِ الْبَرِيدِ، كَانَتْ أُمِّي تَحْمِلُ الطَّابِعَ الآخَرَ.

A rough transliteration is:

ʿindamā kunnā nakhruju min maktabi l-barīdi, kānat ummī taḥmilu ṭ-ṭābiʿa l-ākhara.

A few helpful notes:

• الطابع is pronounced with assimilation of ال because ط is a sun letter, so it sounds like aṭ-ṭābiʿ
• الطابعَ الآخرَ is in the accusative here because it is the direct object of تحمل