You and your friend are walking down the street and you see what looks like a famous person, surrounded by photographers. So you say to your friend:
You: Is he anybody?
Your friend: yes, he's somebody but I can't remember who.
You: What about the man behind him?
Your friend: Oh, him? He's nobody.
Anybody and somebody both mean a person of some importance but those words do not have to refer to famous people. This could refer to the right person to give you a job. For example, "He can help you get a job in advertising. He's somebody you should know."
And finally, nobody means an unimportant person.