Tämä on kirjasto, josta lainaan kirjoja.

Finnish does not use articles the way English does, so there is no separate word for a or the.

• kirjasto just means library
• whether English uses a library or the library depends on context
• tämä already points to a specific thing, so English often ends up using a definite translation such as this is the library...

So Finnish leaves article-like meaning to context, word choice, and situation.

Here kirjasto is in the nominative singular, the basic dictionary form.

That is normal in an affirmative sentence like this, where something is being identified or classified:

• Tämä on kirjasto. = This is a library / the library.

Both tämä and kirjasto are singular, and kirjasto works as the predicative noun after on.

josta is the elative form of the relative pronoun joka.

• joka = which / that / who
• elative -sta / -stä often means from or out of

So:

• joka → josta
• here it means from which

In other words, josta lainaan kirjoja literally means from which I borrow books.

Because the relative pronoun must take the case required by its role inside the relative clause.

The basic non-relative version would be:

• Lainaan kirjoja kirjastosta. = I borrow books from the library.

When kirjastosta is replaced by a relative pronoun, the pronoun has to stay in the same case:

• kirjastosta → josta

So josta is used because the idea is from the library, not just the library as a plain subject or object.

Because mistä and josta belong to different pronoun sets.

• mistä = from where / from what in questions or non-relative expressions
• josta = from which / from where as a relative pronoun

Compare:

• Mistä lainaat kirjoja? = Where do you borrow books from?
• Tämä on kirjasto, josta lainaan kirjoja. = This is the library from which I borrow books.

So mistä is for asking, while josta links back to kirjasto.

lainaan is the 1st person singular present tense of lainata.

• lainata = to borrow / to lend
• lainaan = I borrow / I lend

The ending -n tells you the subject is I, so Finnish does not need the pronoun minä unless you want emphasis.

Because the verb ending already shows the person.

In Finnish, personal pronouns are often omitted when the verb form makes the subject clear:

• lainaan = I borrow
• lainaat = you borrow
• lainaa = he/she/it borrows

So josta lainaan kirjoja is completely natural. You could say josta minä lainaan kirjoja, but that adds emphasis to I.

kirjoja is the plural partitive of kirja.

It is used here because the sentence refers to an indefinite number of books, roughly books / some books, not a specific complete set.

Compare:

• lainaan kirjoja = I borrow books / some books
• lainaan kirjat = I borrow the books / all the books

So the partitive plural is very natural when talking about borrowing books in general.

Yes. Finnish lainata can mean either borrow or lend, and the context tells you which meaning is intended.

In this sentence, it clearly means borrow, because the structure shows a source:

• josta lainaan kirjoja = from which I borrow books

If you are giving something to another person, the same verb can mean lend:

• Lainaan kirjan ystävälle. = I lend a book to a friend.

So you have to look at the whole sentence, not just the verb by itself.

Because josta lainaan kirjoja is a relative clause describing kirjasto.

Finnish normally separates this kind of clause with a comma:

• Tämä on kirjasto, josta lainaan kirjoja.

The relative clause adds extra information about which library is meant: it is the one from which I borrow books.

The given word order is the most neutral and natural one.

• Tämä on kirjasto, josta lainaan kirjoja.

But Finnish word order is fairly flexible, especially for emphasis. For example, you could say:

• Tämä on kirjasto, josta minä lainaan kirjoja.

That emphasizes minä a bit more. Still, the original sentence is the best basic model for a learner.