كان الطابع الصغير في صندوق قرب الباب.

كان is the past-tense form of to be here, so it makes the sentence refer to the past: was.

This sentence is based on a nominal sentence: الطابع الصغير في صندوق قرب الباب = The small stamp is in a box near the door

When you add كان, it becomes: كان الطابع الصغير في صندوق قرب الباب = The small stamp was in a box near the door

A useful point for learners: in the present tense, Arabic usually does not use a word for is/are in simple sentences like this, but in the past tense it does use كان.

In Arabic, adjectives normally come after the noun they describe.

So:

• الطابع الصغير = the small stamp
• not الصغير الطابع

This is the normal noun + adjective order in Arabic.

Because Arabic adjectives must agree with the noun they describe in definiteness as well as gender, number, and case.

So:

• الطابع الصغير = the small stamp
• طابع صغير = a small stamp

This is very important, because:

• الطابع الصغير means the adjective is attached to the noun: the small stamp
• الطابع صغير means The stamp is small

So if only the first word has الـ, you no longer have noun + adjective; you have a complete sentence.

Arabic has a word for the (الـ), but it does not have a separate word for a/an.

So:

• صندوق can mean a box
• الصندوق means the box

That is why في صندوق means in a box, even though there is no separate word for a.

قرب literally has the idea of nearness or close to, and in sentences like this it works as an expression of place: near.

So:

• قرب الباب = near the door

Grammatically, الباب is connected to قرب in an iḍāfa-like relationship, so الباب is in the genitive.

A more explicit alternative you may also see is:

بالقرب من الباب = near the door

Both are natural, but قرب الباب is shorter.

Most naturally, it describes the box.

So the structure is understood as:

• في صندوق = in a box
• قرب الباب = near the door

Together: in a box near the door

In other words, the box is near the door, and the stamp is in that box.

As in English, context can sometimes affect interpretation, but this is the most natural reading here.

A fully vocalized version would be:

كانَ الطّابِعُ الصَّغيرُ في صُنْدوقٍ قُرْبَ البابِ

Here is the grammar:

• كانَ = past-tense was
• الطّابِعُ = ism kāna (the noun of كان), so it is nominative
• الصَّغيرُ = adjective describing الطابع, so it matches and is also nominative
• في صُنْدوقٍ = after the preposition في, so صندوق is genitive
• قُرْبَ البابِ = expression of place; البابِ is genitive

Also note: the predicate of كان here is not a single adjective or noun, but the whole phrase في صندوق قرب الباب.

This is because of sun letters and moon letters.

• ط is a sun letter, so in الطابع the l sound of الـ is not pronounced. The pronunciation becomes roughly aṭ-ṭābiʿ.
• ب is a moon letter, so in الباب the l sound is pronounced: al-bāb.

The spelling stays the same with الـ, but the pronunciation changes depending on the next letter.

It is best understood as a nominal sentence made past by كان.

The basic nominal sentence is:

الطابع الصغير في صندوق قرب الباب

Then كان is added to put it in the past:

كان الطابع الصغير في صندوق قرب الباب

So although the sentence begins with a verb-like word, the core structure is still that of a nominal sentence: a topic/entity plus information about its location.