Mi legas artikolon pri la urbo en la biblioteko.

Because artikolon is the direct object of the verb legas.

In Esperanto, the -n ending marks the thing directly affected by the action.
Here:

• Mi = I
• legas = read / am reading
• artikolon = an article

So artikolon is the thing being read, which is why it takes -n.

A very similar example:

• Mi vidas hundon. = I see a dog.
• Mi manĝas pomon. = I am eating an apple.

In each case, the noun receiving the action gets -n.

Because la means the, and Esperanto has no separate word for a/an.

So:

• artikolon = an article / a article in function, though in English we say an article
• la urbo = the city

The sentence is talking about:

• some article, not a specific one already identified: artikolon
• a specific city: la urbo

If you wanted the article, you would say:

• Mi legas la artikolon pri la urbo.

So the presence or absence of la tells you whether the noun is definite.

Pri means about or concerning.

So:

• artikolo pri la urbo = an article about the city

It introduces the topic of the article.

Compare:

• libro pri historio = a book about history
• paroli pri muziko = to talk about music
• demando pri la lingvo = a question about the language

A learner might wonder whether de could be used, but de usually means of, from, or shows origin/possession. For topic meaning, pri is the normal choice.

It can mean either one, depending on context.

Esperanto present tense -as does not force the same distinction English does between:

• I read
• I am reading

So Mi legas can mean:

• I read
• I am reading

Usually the context makes it clear.

If needed, Esperanto can make things more explicit with adverbs or other wording, but in ordinary language legas is often enough.

Literally, en la biblioteko means in the library.

However, depending on context, English might naturally translate it as in the library or sometimes at the library.

In Esperanto:

• en = in, inside

So the basic idea is physical location inside the library.

Examples:

• Mi estas en la domo. = I am in the house.
• Ŝi studas en la universitato. = She studies at/in the university.

In your sentence, en la biblioteko tells where the reading is happening.

Because en la biblioteko is a prepositional phrase, and biblioteko is not the direct object of the verb.

Here:

• artikolon is what is being read, so it gets -n
• en la biblioteko tells the location, so biblioteko stays without -n

After a preposition like en, the noun normally does not take -n unless there is a special reason, especially movement toward something in some constructions.

So:

• Mi legas en la biblioteko. = I am reading in the library.
• Mi iras en la bibliotekon. = I go into the library.

In the second sentence, -n can show movement into a place.

Yes, technically a learner might wonder about that.

The phrase en la biblioteko comes after la urbo, so you may ask whether it describes:

1. the action of reading, or
2. the city

In real usage, it will almost always be understood as describing where the reading happens:

• I am reading an article about the city, in the library.

Why? Because a city in the library is a strange idea, while reading in the library is completely natural.

Still, if someone wanted to remove all ambiguity, they could change the word order:

• En la biblioteko mi legas artikolon pri la urbo.

That makes the location of the reading even clearer.

Yes. Esperanto word order is fairly flexible.

Because the grammar is shown by endings and prepositions, you can move parts of the sentence around for emphasis or style.

For example, all of these are possible:

• Mi legas artikolon pri la urbo en la biblioteko.
• En la biblioteko mi legas artikolon pri la urbo.
• Artikolon pri la urbo mi legas en la biblioteko.

These all keep basically the same meaning, but the emphasis changes a bit.

The most neutral order is usually the original one:

• subject + verb + object + other details

Because Esperanto uses:

• la for the
• nothing at all for a/an

So:

• artikolo = an article / a article
• la artikolo = the article

This is normal in Esperanto. English learners sometimes expect both the and a/an, but Esperanto only marks definiteness, not indefiniteness.

More examples:

• Mi havas libron. = I have a book.
• Mi havas la libron. = I have the book.

Here is the breakdown:

• Mi — pronoun, meaning I
• legas — verb in the present tense, from legi = to read
• artikolon — noun (artikolo) with -n because it is the direct object
• pri — preposition, meaning about
• la — definite article, meaning the
• urbo — noun, meaning city
• en — preposition, meaning in
• la — definite article again
• biblioteko — noun, meaning library

This kind of breakdown is very useful in Esperanto because the endings are so regular:

• -o = noun
• -as = present-tense verb
• -n = accusative/direct object

A very clear version would be:

• En la biblioteko mi legas artikolon pri la urbo.

Putting En la biblioteko first highlights the location and makes it obvious that it belongs to the action of reading.

Another possible version is:

• Mi legas en la biblioteko artikolon pri la urbo.

But the first rewording is usually smoother and clearer.

So if clarity is your goal, fronting the location phrase is often a good choice.