Post pluviam mensa siccanda est, quia stillae aquae in mensa manent.

Because post is a preposition that takes the accusative when it means after in time or place. So:

• post pluviam = after the rain

A native English speaker may expect something like after rain with no case change, but in Latin prepositions usually control a specific case, and post regularly takes the accusative.

Because the Latin expression is built as a passive periphrastic, not as an active sentence.

• mensa siccanda est literally means the table is to-be-dried
• more naturally: the table must be dried

So mensa is the subject of the sentence, which is why it is nominative. In English, we often prefer an active idea like someone must dry the table, but Latin often expresses this kind of necessity with the thing needing the action as the subject.

Siccanda est is made of:

• siccanda = the gerundive of siccare, meaning to be dried or needing to be dried
• est = is

Together they form a construction that expresses necessity or obligation:

• mensa siccanda est = the table must be dried
• literally: the table is needing to be dried

This is one of the most common Latin ways to say that something has to be done.

Because the gerundive must agree with mensa.

Mensa is:

• feminine
• singular
• nominative

So the gerundive must also be:

• feminine
• singular
• nominative

That gives siccanda.

If the noun were masculine, you would expect siccandus; if neuter, siccandum.

Latin certainly can express obligation in other ways, but this construction is very idiomatic and common.

The passive periphrastic focuses on what needs to be done, rather than on who must do it. So:

• mensa siccanda est = the table must be dried

It leaves the doer unspecified unless Latin wants to mention that person separately, often with the dative of agent:

• mihi mensa siccanda est = I must dry the table
  literally: the table is to be dried by me

That is different from English, where we usually make the person the subject.

This is a very common Latin pattern: a noun followed by a genitive showing what something is made of or consists of.

• stillae = drops
• aquae = of water

So stillae aquae means drops of water.

Here aquae is genitive singular. English uses of, but Latin often uses the genitive case instead.

Because the word water is being treated as a substance, not as separate individual waters.

So Latin says:

• stillae aquae = drops of water

The number of drops is shown by stillae being plural. The substance itself, water, stays singular, just as English normally says drops of water, not drops of waters.

Latin in with the ablative can mean either in or on, depending on context.

So:

• in mensa can mean on the table or in the table
• in this sentence, because we are talking about water drops, the natural meaning is on the table

Latin does not always distinguish in and on as strictly as English does. Context tells you which meaning is intended.

Because it has a different grammatical role the second time.

First:

• mensa in mensa siccanda est is nominative
• it is the subject: the table

Second:

• mensa in in mensa is ablative
• it is the object of the preposition in: on the table

The form happens to look the same in the first declension:

• nominative singular: mensa
• ablative singular: mensa

So even though the spelling is identical, the function is different.

Because manere means to remain, to stay, or to continue to be present.

So:

• stillae aquae in mensa manent = drops of water remain on the table

This gives a more specific idea than sunt. It suggests that the water drops are still there after the rain, which explains why the table needs drying.

Quia means because and introduces a clause giving the reason.

So the sentence is structured like this:

• Post pluviam mensa siccanda est = After the rain, the table must be dried
• quia stillae aquae in mensa manent = because drops of water remain on the table

It is simply a causal conjunction linking the explanation to the main statement.

Latin word order is much more flexible than English word order because Latin endings show grammatical relationships.

This sentence puts the time expression first:

• Post pluviam = After the rain

Then the main idea:

• mensa siccanda est = the table must be dried

Then the reason:

• quia stillae aquae in mensa manent = because drops of water remain on the table

This order is perfectly natural in Latin. English relies heavily on word order for grammar, but Latin uses endings, so word order is freer and often used for emphasis or style.

Classical Latin has no definite article and no indefinite article in the way English does.

So:

• mensa can mean table, a table, or the table
• pluviam can mean rain, a rain, or the rain

You decide from the context which English article is best. In this sentence, English naturally uses the:

• after the rain
• the table
• the water drops

But Latin does not need separate words for those articles.