Here's an example:
Your first language is Arabic. You also know two other languages: English and French.
Hundreds of millions of people speak Arabic as their first language, but they speak different variants of Arabic, for example Gulf Arabic and Levantine Arabic. Pronunciation, grammar and vocabulary vary from one dialect to another. Sometimes dialects of the same language are mutually comprehensible, sometimes they aren't.
An accent is only about the way someone sounds when they speak: pronunciation, and also other features such as stress and intonation. For example, when you speak English, you speak with an Arabic accent: this means that you 'sound' Arabic, even when using English words and grammar. If I were to learn Arabic and speak to you, I'd speak with an English accent. An Egyptian man living in Algeria might sound Egyptian to your ear, even when he is speaking Algerian Arabic to you.
I hope that helps.