On my report there is a date that the account was opened and then there is a date that the account is closed. The date opened is 11/2002 and the closd date is 6/2003, do I need to pay this amount or what? I am so confused about all of this? Please help.

An account being closed does not mean you don't owe, it means you can no longer charge on it.
Even if it said "charged off" that is a tax term and does not mean you don't owe it.

Now depending on where you live and the type of debt, they may or may not be able to take you to court and get a judgement on a old debt ( the SOL may or may not be out)

But even if it is past the SOL, you still owe it, they can still try and collect they just can't sue you.