In foco cinis manet post cenam.

Because in foco uses in to mean in/on in the sense of location, and with that meaning in takes the ablative case.

• focus = hearth, fireplace
• nominative singular: focus
• ablative singular: foco

So in foco means in the hearth or in the fireplace.

If there were motion into the hearth, Latin would normally use the accusative instead: in focum.

Because post is a preposition that takes the accusative case.

• cena = dinner, meal
• accusative singular: cenam

So post cenam means after dinner or after the meal.

This is something you often just have to memorize with prepositions:

• in
  • ablative = in/on, location
• post
  • accusative = after

The subject is cinis.

You can tell because:

• cinis is nominative singular
• the verb manet is third person singular

So cinis manet = the ash remains / ash remains.

Even though English often puts the subject first, Latin does not have to do that. The noun’s ending is what tells you its role.

Manet is:

• third person singular
• present tense
• active voice
• indicative mood

It comes from maneo, manere, meaning remain, stay, or continue to be.

So manet means he/she/it remains or stays.
Here the subject is cinis, so the natural translation is ash remains.

You know from both the noun and the verb.

• cinis is nominative singular
• manet is singular, not plural

If the subject were plural, you would expect something like cineres manent = the ashes remain.

So this sentence is grammatically singular: ash remains.

Because classical Latin does not have articles like English the and a/an.

So:

• cinis can mean ash, the ash, or sometimes an ash
• focus can mean hearth or the hearth
• cena can mean dinner or the dinner/meal

You choose the most natural English wording from the context.

They belong to different declensions:

• focus, foci = second declension masculine
• cena, cenae = first declension feminine
• cinis, cineris = third declension masculine

That is why their endings look different:

• foco = ablative singular second declension
• cenam = accusative singular first declension
• cinis = nominative singular third declension

Cinis usually means ash, ashes, or cinders, depending on context.

Latin often uses a singular where English might prefer a mass noun or even a plural. So all of these can be reasonable in context:

• ash remains
• the ash remains
• ashes remain

In this sentence, singular ash is a very natural choice because the verb is singular: manet.

The case tells you.

With in:

• in + ablative = location: in, on
• in + accusative = motion into: into, onto

Here we have foco, which is ablative. So it means in the hearth as a place where something already is.

If the sentence meant The ash goes into the hearth, Latin would use in focum.

Yes. Latin word order is much freer than English word order because the endings show the grammar.

For example, these would still mean essentially the same thing:

• Cinis in foco manet post cenam.
• Post cenam cinis in foco manet.
• In foco post cenam cinis manet.

However, different word orders can slightly change emphasis.
Starting with In foco puts focus on the place: In the hearth, ash remains after dinner.

Probably for emphasis or style.

Latin often puts important setting information early in the sentence. By starting with In foco, the sentence first establishes where the action is happening.

So the sentence feels a bit like:

• In the hearth, ash remains after dinner.

That is not a different basic meaning, just a different emphasis.

No. In Latin, focus originally means hearth, fireplace, or fireplace area.

The English word focus comes from this Latin word, but in modern English it usually means center of attention or point of concentration. That modern meaning is much later.

So in this sentence, focus has its original concrete meaning: hearth or fireplace.

Yes. Post cenam simply means after dinner or after the meal.

It does not by itself specify exactly how soon after. It could mean:

• immediately after dinner,
• later that evening,
• generally after the meal is over.

The context would decide how precise the time reference is.

A very literal breakdown is:

• In foco = in the hearth
• cinis = ash
• manet = remains
• post cenam = after dinner

So a very literal translation is:

In the hearth ash remains after dinner.

More natural English might be:

• Ash remains in the hearth after dinner.
• The ash stays in the fireplace after the meal.