This means "for the purpose of". Some books will translate this as "for", but this is confusing. Do not think this.

Fizettem húsz dollárt a könyvért. I paid twenty dollars for (the purpose of) this book.

Note that bocsánat means "apology, (a) pardon, forgiveness." We can use "Bocsánat!" to mean, "sorry!" in the sense of "pardon me." When we are apolgising, in the sense of asking to be forgiven, we say bocsánatot kérek I ask for forgiveness.

When there is something specific for which we are apologising, we use the causal-final (-ért) case thus:

• bocsánatot kérek a kutyámért I apologise for my dog. That is, "I am sorry for my dog, I apologise about my dog."

Note that the demonstrative pronouns, particularly azért, litererally mean

• ezért "for this purpose" = herefore
• azért "for that purpose" = therefore

Thus you can use azért to mean "therefore".

If you combine mi (what) with -ért, you get the word miért, "for what purpose".

This is used to mean "why".

When answering a question put with miért?, you should not just say "because....", but literally say "for that reason, because..."

• Miért ide jöttél? Why did you come here? (For what purpose did you come to here?)
• Azért, mert akartam találkozni veled. Because I wanted to meet you. (For that purpose, because I wanted to meet with you.)