Agricola dicit ligna fagi, fraxini, et ulmi bona esse ad focum.

It helps to divide it into two parts:

• Agricola dicit = the main clause
• ligna fagi, fraxini, et ulmi bona esse ad focum = what the farmer says

Inside the second part:

• ligna = the wood / the pieces of wood
• fagi, fraxini, et ulmi = of beech, ash, and elm
• bona esse = to be good
• ad focum = for the hearth/fire

So the whole second part is the content of the statement.

Because agricola is a first-declension masculine noun.

Latin declension and grammatical gender are related, but not identical. Most first-declension nouns are feminine, but some nouns referring to traditionally male occupations or roles are masculine, such as:

• agricola = farmer
• nauta = sailor
• poeta = poet

So agricola is masculine in meaning, even though it has a first-declension ending.

This is a very common Latin construction called indirect statement.

After verbs like dicit (he says), Latin often uses:

• an accusative subject
• plus an infinitive verb

So instead of saying:

• The farmer says that the wood is good for the fire

Latin says, more literally:

• The farmer says the wood to be good for the fire

The direct version would be:

• Ligna fagi, fraxini, et ulmi bona sunt ad focum.

After dicit, sunt changes to esse.

The subject of esse is ligna.

That can be confusing, because in indirect statement the subject is normally put in the accusative. Here, ligna is accusative plural, but it looks exactly like nominative plural because it is a neuter plural noun.

So:

• ligna = nominative plural or accusative plural
• here it is accusative plural as the subject of esse

This is one of those places where Latin form and function are not obvious at first glance.

Ligna is the plural of lignum.

In Latin, the plural ligna often means:

• pieces of wood
• logs
• firewood

So even if English uses the mass noun wood, Latin may use the plural when it is thinking of wood as separate pieces to be burned or used.

In this sentence, the context is fuel for a fire, so ligna is very natural.

They are genitive singular forms:

• fagi = of beech
• fraxini = of ash
• ulmi = of elm

They depend on ligna and tell us what kind of wood it is.

So ligna fagi means beech wood, literally wood of beech.

Latin often uses the genitive this way to show:

• material
• source
• kind

The singular is normal here because Latin is naming the tree species, not counting multiple individual trees.

Because bona agrees with ligna.

Since ligna is:

• neuter
• plural

the adjective describing it must also be:

• neuter
• plural

So:

• lignum bonum = good wood / a good piece of wood
• ligna bona = good wood / good pieces of wood

Also, in this indirect statement, bona is part of the infinitive clause with esse, so it works as a predicate adjective: the wood to be good.

Because the sentence is in indirect statement.

If this were a direct statement, Latin would say:

• ligna ... bona sunt ad focum = the wood is good for the fire

But after dicit, Latin changes the finite verb sunt into the infinitive esse:

• dicit ligna ... bona esse ad focum

So esse is just the indirect-statement version of sunt here.

Ad takes the accusative, so focum is accusative because it follows ad.

The phrase ad focum literally means to/toward the hearth, but in context it means something like:

• for the fire
• for the hearth
• as fuel

Focus originally means hearth or fireplace, and by extension it can suggest the domestic fire itself.

So bona esse ad focum means to be good for burning in the hearth.

Yes, but it is also normal Latin.

Latin word order is more flexible than English because the endings show the grammar. This lets Latin arrange words for clarity, rhythm, or emphasis.

Here:

• Agricola dicit comes first, so we immediately know who is speaking
• ligna fagi, fraxini, et ulmi keeps the noun and its specifying genitives together
• bona esse comes toward the end, where Latin often places an infinitive phrase
• ad focum neatly finishes the idea of purpose or use

So the order may feel unusual to an English speaker, but it is perfectly natural in Latin.