Markete geç gidince sadece bayat ekmek kaldı.

Because gitmek means to go, and destinations usually take the dative case in Turkish.

• market = market
• markete = to the market

The dative ending is -a / -e, chosen by vowel harmony. Since market has a front vowel, it takes -e.

So:

• markete gitmek = to go to the market

Here, geç means late.

In this sentence it works like an adverb, describing how/when the going happened:

• geç gitmek = to go late
• markete geç gidince = when/after going to the market late

So geç is modifying the action gidince.

Gidince comes from gitmek and the suffix -ince.

It means something like:

• when ... goes/went
• after ... going
• sometimes even since/because ... went

So:

• gidince = when/after going

In this sentence, Markete geç gidince means when/after going to the market late.

This -ince form is very common in Turkish for making a time clause.

This is a very common learner question. The verb is dictionary form gitmek, but in some forms the stem appears as gid-.

So you get:

• gitmek
• gidiyor
• gidecek
• gidince

But:

• gitti

A simple way to remember it is:

• before many vowel-initial endings, git- becomes gid-
• before some consonant-initial endings, it stays git-

So gidince is the correct form.

Turkish often leaves out pronouns when the context already makes them clear.

So this sentence does not explicitly say who went late. Depending on context, it could mean:

• when I went to the market late
• when you went to the market late
• when he/she went to the market late

If you want to make it explicit, you can add the pronoun:

• Ben markete geç gidince sadece bayat ekmek kaldı.
• O markete geç gidince sadece bayat ekmek kaldı.

Turkish usually prefers leaving pronouns out unless they are needed for emphasis or clarity.

Because in Turkish, adjectives normally come before the noun they describe.

So:

• bayat ekmek = stale bread
• taze ekmek = fresh bread
• büyük market = big market

This is similar to English word order in adjective + noun combinations.

If you said ekmek bayat, that would not mean stale bread as a noun phrase. It would sound like part of a sentence such as:

• Ekmek bayat. = The bread is stale.

Sadece means only.

Here it comes right before bayat ekmek, so it most naturally emphasizes that noun phrase:

• sadece bayat ekmek kaldı = only stale bread was left

In other words, no fresh bread or other bread remained.

In Turkish, words like sadece are often placed close to the thing they emphasize.

The verb is kalmak, which often means:

• to stay
• to remain
• to be left

In this sentence, the best meaning is was left / remained:

• sadece bayat ekmek kaldı = only stale bread was left

So it does not mean that the bread deliberately stayed somewhere. It means that after the others were gone, stale bread was what remained.

Because Turkish normally puts the main verb at the end of the clause.

The structure here is:

• Markete geç gidince = time clause
• sadece bayat ekmek = subject / thing remaining
• kaldı = main verb

So the whole sentence follows a very normal Turkish pattern: background information first, main verb last.

A rough structure is:

[When going to the market late] [only stale bread] [remained]

It can do both, depending on context.

Most basically, -ince gives a time meaning:

• when
• after

But in real usage, a cause-and-effect idea can also appear:

• Markete geç gidince sadece bayat ekmek kaldı.

This can be understood as:

• When I went to the market late, only stale bread was left
• or more naturally in some contexts, Because I went to the market late, only stale bread was left

So -ince is often primarily temporal, but it can carry a causal feeling too.

Turkish does not have articles that work exactly like English the and a.

That means Turkish often leaves article-like meaning to:

• context
• word order
• case endings
• whether bir is used

For example:

• markete can naturally mean to the market
• bayat ekmek can mean stale bread or the stale bread, depending on context

If Turkish wants to say a/an more clearly, it can use bir:

• bir markete would usually mean to a market
• bir ekmek = a loaf/piece of bread or one bread, depending on context

In your sentence, no article word is needed.