Die geöffnete Brotdose liegt noch auf dem Tisch, obwohl alle schon gegangen sind.

Geöffnete means opened or more naturally open here.

It comes from the verb öffnen = to open.
The form geöffnet is the past participle, and in this sentence it is being used like an adjective before the noun:

• die geöffnete Brotdose = the opened/open lunchbox

In English, we often just say the open lunchbox, but German very commonly uses participles this way.

The ending -e appears because the adjective is in front of a noun with the definite article die, and the noun is feminine singular nominative:

• die Brotdose
• die geöffnete Brotdose

This is a standard adjective ending pattern.

Because of adjective declension.

Here, Brotdose is:

• feminine
• singular
• nominative (it is the subject of the sentence)

And it has the definite article die.

With a definite article, the adjective usually takes a weak ending. For feminine singular nominative, that ending is -e:

• die geöffnete Brotdose

Compare:

• die geöffnete Brotdose
• der geöffnete Kasten
• das geöffnete Fenster

So the ending is not random; it matches the noun’s grammatical role and article.

Brotdose is a compound noun:

• Brot = bread
• Dose = container, box, tin

Together, Brotdose usually means a lunchbox or food container, especially one used to carry bread, sandwiches, or snacks.

German uses compound nouns very freely, so this is a very normal word.

German often uses specific position verbs where English might just use is.

• liegen = to lie, to be lying
• stehen = to stand, to be standing
• sitzen = to sit, to be sitting

So:

• Die Brotdose liegt auf dem Tisch
  = The lunchbox is lying on the table
  = more naturally in English: The lunchbox is on the table

German often cares about the object’s physical position more explicitly than English does. A lunchbox is thought of as something lying flat, so liegen is natural.

Here, noch means still.

• Die geöffnete Brotdose liegt noch auf dem Tisch
  = The open lunchbox is still on the table

It suggests that the lunchbox remains there, even though you might expect it not to be there anymore.

That fits well with the second clause:

• obwohl alle schon gegangen sind = although everyone has already left

So there is a contrast:

• everyone has left,
• but the lunchbox is still there.

Because auf is a two-way preposition.

Two-way prepositions take:

• dative for location
• accusative for movement toward a destination

Here, the lunchbox is already located on the table, so this is location, not movement:

• auf dem Tisch = on the table → dative

Compare:

• Die Brotdose liegt auf dem Tisch.
  The lunchbox is on the table.
• Ich lege die Brotdose auf den Tisch.
  I put the lunchbox onto the table.

So:

• wo? (where?) → dative
• wohin? (to where?) → accusative

Because obwohl introduces a subordinate clause, and in German subordinate clauses are separated by a comma.

So:

• Die geöffnete Brotdose liegt noch auf dem Tisch, obwohl alle schon gegangen sind.

This comma is required in standard German.

The word obwohl means although or even though, and it introduces a clause that contrasts with the main statement.

Because obwohl is a subordinating conjunction.

In German, subordinating conjunctions send the conjugated verb to the end of the clause.

Main clause:

• Die Brotdose liegt noch auf dem Tisch.
• Verb position: second

Subordinate clause:

• obwohl alle schon gegangen sind
• Finite verb sind goes to the end

This is one of the most important word-order rules in German.

Other common subordinating conjunctions that do the same thing:

• weil = because
• dass = that
• wenn = if/when
• ob = whether

Because this is a subordinate clause.

In the normal perfect tense in a main clause, you often see:

• Alle sind schon gegangen.

But after obwohl, the clause becomes subordinate, so the finite verb moves to the end:

• obwohl alle schon gegangen sind

In the perfect tense, that means:

• past participle gegangen
• auxiliary sind at the very end

So both of these are the same tense, just with different word order:

• Alle sind schon gegangen.
• ..., obwohl alle schon gegangen sind.

Because gehen forms the perfect tense with sein, not haben.

So:

• ich bin gegangen
• du bist gegangen
• wir sind gegangen

Many verbs of movement or change of state use sein in the perfect tense.

Since alle means everyone/all of them, it is grammatically plural here, so the sentence uses:

• alle ... sind gegangen

Here, alle means something like everyone or all of them, depending on context.

• obwohl alle schon gegangen sind
  = although everyone has already left
  or
  = although they have all already left

German alle can work as a pronoun on its own when the group is understood.

So you do not need a noun after it. It can stand alone:

• Alle sind da. = Everyone is here.
• Alle sind gegangen. = Everyone has left.

Schon here means already.

• alle schon gegangen sind
  = everyone has already left

It shows that the leaving happened earlier than the point being discussed.

Together, noch and schon create a nice contrast:

• noch = still
• schon = already

So the sentence contrasts two states:

• the lunchbox is still on the table,
• although everyone has already left.