Die Pfannkuchen bleiben auf dem Backblech warm, solange die anderen noch essen.

Because bleiben means to remain or to stay.

• Die Pfannkuchen sind warm = the pancakes are warm.
• Die Pfannkuchen bleiben warm = the pancakes stay/remain warm.

So bleiben adds the idea that the warmth continues for some time.

Die Pfannkuchen is the subject of the sentence.

• Pfannkuchen is plural
• the plural definite article is die

So die Pfannkuchen means the pancakes.

You can also see that it is the subject because the verb is bleiben, which is plural here to match Pfannkuchen.

In a normal German main clause, the finite verb goes in second position.

Here the sentence begins with the subject:

• Die Pfannkuchen = position 1
• bleiben = position 2

That is standard German word order:

• Die Pfannkuchen bleiben ...

Because auf is a two-way preposition. It can take:

• dative for location
• accusative for movement toward a destination

Here the pancakes are already on the baking tray; this is a location, not movement. So German uses dative:

• auf dem Backblech = on the baking tray

Compare:

• Die Pfannkuchen liegen auf dem Backblech. = They are on the tray.
• Ich lege die Pfannkuchen auf das Backblech. = I put them onto the tray.

Because warm is not being used before a noun here. It is a predicate adjective, used with the linking verb bleiben.

In German, predicate adjectives do not take adjective endings:

• Die Pfannkuchen bleiben warm.

But when an adjective comes before a noun, it does take an ending:

• die warmen Pfannkuchen

So:

• warm = predicate adjective, no ending
• warmen = attributive adjective before a noun

Solange means as long as or, in this context, very naturally while.

It introduces a time relationship:

• the pancakes stay warm
• for the period during which the others are still eating

So it connects the two actions in time.

Because solange introduces a subordinate clause, and in German subordinate clauses the finite verb usually goes to the end.

Main clause:

• Die Pfannkuchen bleiben auf dem Backblech warm

Subordinate clause:

• solange die anderen noch essen

Inside that subordinate clause:

• die anderen = subject
• noch = still
• essen = verb at the end

This verb-final pattern is very common after words like weil, dass, wenn, obwohl, and solange.

It means the others or the other people.

German often leaves out a noun when it is obvious from context. So die anderen here really means something like:

• die anderen Personen
• die anderen Leute
• the others

In this sentence, it refers to the other people who are still eating.

Noch here means still.

So:

• die anderen essen = the others are eating
• die anderen noch essen = the others are still eating

It suggests that their eating is continuing at that moment.

Because German normally uses a comma before a subordinate clause.

Since solange die anderen noch essen is a subordinate clause, the comma is required:

• Die Pfannkuchen bleiben auf dem Backblech warm, solange die anderen noch essen.

This is a very common punctuation rule in German.

Because essen can be used without stating what is being eaten when the meaning is obvious.

Just like English can say:

• They’re still eating.

German can also simply say:

• Sie essen noch.

The object is understood from the situation, so it does not need to be named.