Mater pannum humidum capit et mensam tergit.

Mater is the subject of the sentence, so it is in the nominative case.

• mater = mother as the one doing the action
• matrem would mean mother as a direct object

In this sentence, the mother is doing the actions of capit and tergit, so mater must be nominative.

They are both direct objects, so they are in the accusative case.

The sentence has two actions:

• capit = takes
• tergit = wipes

So:

• pannum humidum is what the mother takes
• mensam is what the mother wipes

In Latin, direct objects are usually put in the accusative.

Humidum is an adjective modifying pannum, so it has to agree with it in:

• gender
• number
• case

Here:

• pannum is masculine
• singular
• accusative

So the adjective must also be masculine singular accusative:

• pannus humidus = a wet cloth (nominative)
• pannum humidum = a wet cloth (accusative)

Latin usually does not have articles like English the or a/an.

So:

• mater can mean mother, a mother, or the mother
• pannum humidum can mean a wet cloth or the wet cloth
• mensam can mean a table or the table

You figure out which is meant from the context.

In Latin, adjectives can come before or after the noun. Both are common.

So pannum humidum means wet cloth, even though English usually puts the adjective first.

Latin word order is more flexible because the endings show the grammar. The important thing is not the position, but the agreement:

• pannum = masculine singular accusative
• humidum = masculine singular accusative

That shows they belong together.

Capit is:

• 3rd person singular
• present tense
• active voice
• from the verb capere = to take

It means he/she/it takes.

Here the subject is mater, so it means mother takes or the mother takes.

Tergit is also:

• 3rd person singular
• present tense
• active voice

It comes from tergere, meaning to wipe or to clean by wiping.

So mensam tergit means she wipes the table.

Latin often uses one subject with more than one verb.

Here:

• mater ... capit
• et ... tergit

The subject mater applies to both verbs:

• Mother takes the wet cloth
• and wipes the table

Latin does not need to repeat mater because it is already clear that the same person is doing both actions.

Et means and.

It joins the two actions:

• capit = takes
• tergit = wipes

So it connects the ideas:

Mother takes the wet cloth and wipes the table.

Yes, often they could.

Because Latin uses case endings, word order is more flexible than in English. For example, these would still mean basically the same thing:

• Mater pannum humidum capit et mensam tergit.
• Pannum humidum mater capit et mensam tergit.
• Mater mensam tergit et pannum humidum capit.
  (This changes the order of the actions, but not the basic grammar.)

However, changing the order can change the emphasis or style.

Because of agreement.

• pannum is masculine singular accusative
• humidum is also masculine singular accusative

But:

• mensam is feminine singular accusative

If the adjective described mensam, it would need to be humidam, not humidum.

So the grammar tells you that humidum modifies pannum.

No. Mater is not a first-declension noun.

It belongs to the third declension. Some common forms are:

• mater = nominative singular
• matris = genitive singular
• matrem = accusative singular

This is a good reminder that Latin nouns are grouped by their full pattern of endings, not just by what the nominative singular happens to look like.

A common classroom pronunciation would be roughly:

MAH-ter PAN-num hoo-MEE-dum KAH-pit et MEN-sam TER-git

A few notes:

• c in capit is always hard, like k
• g in tergit is always hard, like in get
• h in humidum is very light or sometimes barely heard in many teaching traditions
• stress usually falls as follows:
  • máter
  • pánnum
  • humídum
  • cápit
  • ménsam
  • térgit

If your course uses a specific pronunciation system, follow that system consistently.