На полке стоит ряд книг.

Because after на when it means in/on a location, Russian uses the prepositional case.

• полка = shelf (dictionary form, nominative)
• на полке = on the shelf

So:

• На полке = on the shelf

If на showed motion onto the shelf, Russian would usually use the accusative instead:

• на полку = onto the shelf

Because the grammatical subject here is ряд, not книг.

• ряд = row, line, series
• книг = of books

So the phrase ряд книг literally means a row of books. The head word is ряд, and it is singular masculine, so the verb is also singular:

• ряд стоит = the row stands

Even though the meaning involves multiple books, Russian grammar agrees with ряд.

Because ряд requires the next noun to be in the genitive case.

• книги can be nominative plural or genitive singular depending on context
• книг is genitive plural

After words like ряд (a row of), много (many), несколько (several), Russian often uses the genitive.

So:

• ряд книг = a row of books
• literally: row of books

Russian often uses verbs of position more specifically than English.

• стоять = to stand
• лежать = to lie
• сидеть = to sit

Books placed upright on a shelf are naturally described with стоять in Russian.

So:

• Книги стоят на полке. = The books are on the shelf.
  • literally: The books are standing on the shelf.

If the books were lying flat, Russian would more likely use лежать.

Yes. That is often the most natural English translation.

Russian commonly uses sentences like this without a word meaning there is:

• На полке стоит ряд книг.

Depending on context, natural English could be:

• There is a row of books on the shelf.
• A row of books is standing on the shelf.
• A row of books stands on the shelf.

The last one is more literal, but the first is often the most natural in English.

Russian word order is flexible. Starting with На полке puts the location first.

This is very common when introducing what is present somewhere:

• На полке стоит ряд книг. = On the shelf, there is a row of books.

If you say:

• Ряд книг стоит на полке.

that is also correct, but it feels more like you are talking specifically about the row of books and then saying where it is.

So the original sentence has a natural location-first, existence/presence feel.

Grammatically, yes, but it is often less natural in this kind of sentence.

Russian frequently omits есть when simply stating that something exists somewhere in the present tense.

So Russian usually prefers:

• На полке стоит ряд книг.

rather than:

• На полке есть ряд книг.

Also, стоит gives extra information: the books are arranged upright/standing. Есть only says that the row exists there.

Here ряд means a row, a line, or a series of things arranged together.

In this sentence:

• ряд книг = a row of books

Depending on context, ряд can also mean things like:

• a series
• a number of
• a range

But in this shelf context, row of books is the most likely meaning.

They are both natural, but they mean slightly different things.

• На полке стоят книги. = There are books on the shelf.
• На полке стоит ряд книг. = There is a row of books on the shelf.

The second one is more specific. It emphasizes that the books form a row rather than just being present.

Ряд is in the nominative singular because it is the subject of the sentence.

Breakdown:

• На полке — prepositional case, showing location
• стоит — 3rd person singular present of стоять
• ряд — nominative singular, the subject
• книг — genitive plural, dependent on ряд

So the grammatical skeleton is:

• [Where?] На полке
• [What is there / what stands there?] ряд книг

The standard stress is:

• На пОлке стоИт ряд книг.

Word by word:

• на
• пОлке
• стоИт
• ряд
• книг

Stress matters in Russian, so this is worth learning early.

Russian has no articles like a or the, so context decides that.

The sentence could mean:

• There is a row of books on the shelf
• A row of books is on the shelf
• sometimes even The row of books is on the shelf, if the context already makes it definite

English forces you to choose an article, but Russian usually does not.

That would sound unusual in normal modern Russian.

Russian word order is flexible, but not completely free. The neutral, natural version is:

• На полке стоит ряд книг.

You may also hear:

• Ряд книг стоит на полке.

But стоит книг ряд is highly marked and poetic/literary at best. For everyday Russian, stick with the normal order.