Learn Spanish (Spain): El libro es grande.

In Spanish, every noun has a gender. Because libro ends in -o, it is usually a masculine noun. The word for "the" that goes with masculine, singular nouns is el.

We learned that es means "he is" or "she is". Why is it used for a book?

Es is the form of the verb ser (to be) used for any single person, place, or thing. Just like it means "he is" or "she is", it also translates to "it is" when talking about an object like el libro.

Since el libro is masculine, shouldn't the word for "big" end in -o (like grando)?

Not all adjectives change their endings to match gender. Adjectives that already end in -e, like grande, stay exactly the same whether they are describing a masculine noun (like el libro) or a feminine noun (like la casa).

How would I say "This is big" if I didn't want to use the word "book"?

If you want to say "this" without naming the specific object, you use the neuter pronoun esto. Following the exact same word order, the sentence would simply become Esto es grande (This is big).