На столе остались крошки от батона, и я быстро вытерла их салфеткой.

Because на столе answers the question where? and expresses location, so Russian uses the prepositional case here.

• на столе = on the table
• на стол would mean onto the table, expressing direction or movement toward the surface

Compare:

• Крошки лежат на столе. = The crumbs are on the table.
• Я положила салфетку на стол. = I put the napkin onto the table.

In this sentence, the crumbs are already there, so на столе is required.

Остались is the past tense plural form of остаться, which means to remain, to be left, or to stay behind.

It is plural because the subject is крошки (crumbs), which is plural.

So:

• крошки остались = crumbs remained / crumbs were left

Russian past tense agrees with the subject in number, and in the singular it also agrees in gender:

• крошка осталась = one crumb remained
• крошки остались = crumbs remained

Because остались gives the idea that the crumbs were left behind or still there, not just that they existed.

Compare:

• На столе были крошки. = There were crumbs on the table.
  This is more neutral: it simply states their presence.
• На столе остались крошки. = Crumbs were left on the table / There were still crumbs left on the table.
  This suggests something happened before, and the crumbs remained afterward.

So остались adds a sense of result or aftermath.

Because крошки is the subject of the first clause.

In На столе остались крошки, the thing that remained is the crumbs, so that noun is in the nominative case:

• крошки = nominative plural

Even though English often says There were crumbs on the table, Russian does not need a dummy subject like there. The real subject is just крошки.

Not exactly. Батон usually means a long loaf of white bread in Russian, especially the common sliced bread loaf sold in stores.

So крошки от батона means:

• crumbs from a loaf of bread
• often more specifically crumbs from a white bread loaf

It is a very common everyday Russian word, but it does not perfectly match the English word loaf in every situation.

Батона is in the genitive case because it follows от, which here means from.

• от + genitive = from, off, from the source of something

So:

• от батона = from the loaf
• крошки от батона = crumbs from the loaf

This is a very common pattern in Russian:

• запах от супа = smell from the soup
• ключ от машины = key to/for the car
• тень от дерева = shadow from the tree

Вытерла is the past tense feminine singular form of вытереть (to wipe off / wipe up / wipe away).

The ending -ла tells us the speaker is female, because the subject is я and in the past tense Russian verbs agree with the speaker’s gender.

Compare:

• я вытерла = I wiped (female speaker)
• я вытер = I wiped (male speaker)

So this sentence tells us that the person speaking is a woman or girl.

Их means them, referring back to крошки (crumbs).

Here it is the direct object of вытерла, so its function is accusative:

• я вытерла их = I wiped them up

With the pronoun их, the form is the same for both genitive and accusative, so the form itself does not change here. You understand its role from the verb and context.

Because салфеткой is the instrumental case, used to show the tool or means by which the action is done.

So:

• салфетка = napkin (nominative)
• салфетку = napkin (accusative, as a direct object)
• салфеткой = with a napkin / using a napkin (instrumental)

The verb вытереть often takes the pattern:

• вытереть что? чем?
• wipe what? with what?

So:

• вытерла их салфеткой = wiped them up with a napkin

Because the sentence describes completed events in sequence.

• остаться is perfective: the crumbs ended up being left behind
• вытереть is perfective: the speaker wiped them up completely

This is very natural in narration when you are reporting finished actions and results.

If you used imperfective forms, the meaning would shift:

• оставались would suggest an ongoing state or repeated situation
• вытирала would suggest the process of wiping, or repeated wiping, rather than the completed result

So the perfective aspect fits the idea:

1. crumbs were left on the table
2. then I quickly wiped them up

Both are possible, but the word order changes the focus.

• На столе остались крошки puts the location first and sounds very natural if the table is already the topic.
• Крошки остались на столе puts more emphasis on the crumbs.

Russian word order is flexible, and it often reflects information structure rather than strict grammatical rules.

In this sentence, starting with На столе feels natural because it sets the scene first:

• On the table, there were crumbs left...

Because и is joining two separate clauses, each with its own predicate:

1. На столе остались крошки от батона
2. я быстро вытерла их салфеткой

Russian normally uses a comma before и when it connects two independent clauses.

So the comma is needed here just as in English:

• Crumbs were left on the table, and I quickly wiped them up with a napkin.

It mainly means quickly, but it also adds a small nuance: the speaker reacted promptly and cleaned the crumbs without delay.

So:

• я вытерла их = I wiped them up
• я быстро вытерла их = I quickly wiped them up

In Russian, быстро is very common and neutral. It simply adds manner to the action.

Its position is flexible:

• я быстро вытерла их
• я их быстро вытерла

Both are possible, though the first is the most neutral here.